· 2011. 3. 31. · SUMMARY The Skill of Bicycle Riding A.J.R. Doyle The principal theories of human motor skill are compared. Disagreements between them centre around the exact

THE SKILL OF BICYCLE RIDING

Anthony John Redfern Doyle

Department of psychology, University of Sheffield

Submitted in part fulfilment of the requirements of the degree of PhD.

March 1987

SUMMARY

The Skill of Bicycle Riding

A.J.R. Doyle

The principal theories of human motor skill are compared. Disagreements between them centre around the exact details of the feedback loops used for control. In order to throw some light on this problem a commonplace skill was analysed using computer techniques to both record and model the movement. Bicycle riding was chosen as an example because it places strict constraints on the freedom of the rider's actions and consequently allows a fairly simple model to be used. Given these constraints a faithful record of the delicate balancing movements of the handlebar must also be a record of the rider's actions in controlling the machine.

An instrument pack, fitted with gyroscopic sensors and a handlebar potentiometer, recorded the roll, yaw and steering angle changes during free riding in digital form on a microcomputer disc. A discrete step computer model of the rider and machine was used to compare the output characteristic of various control systems with that of the experimental subjects. Since the normal bicycle design gives a measure of automatic stability it is not possible to tell how much of the handlebar movement is due to the rider and how much to the machine. Consequently a bicycle was constructed in which the gyroscopic and castor stability were removed. In order to reduce the number of sensory contributions the subjects were blindfolded.

The recordings showed that the basic method of control was a combination of a continuous delayed repeat of the roll angle rate in the handle-bar channel, with short intermittent ballistic acceleration inputs to control angle of lean and consequently direction.

A review of the relevant literature leads to the conclusion that the proposed control system is consistent with current physiological knowledge. Finally the bicycle control system discovered in the experiments is related to the theories of motor skills discussed in the second chapter.

Acknowledgements

This thesis was supported by a studentship grant from

the Science and Engineering Research Council. I gratefully

acknowledge the direction and support of my supervisor

Professor Kevin Connolly. I would also like to thank Bob

Chapman and Mick Cruse of the psychology technical

department for turning my vague notions into working

hardware, and especial thanks is due to Michael Port who

not only constructed the recording module and kept it

running, but also showed great patience in acting as one

of the test subjects.

Professor Linkens of the Control Engineering department

provided generous support, as did Dr. Neal of the

Mechanical Engineering department. I would also like to

thank my son James, my daughter Harriet and my

granddaughter Hannah for acting as experimental subjects.

I would very much like to thank Chris Brown and Max

Westby for their quite exceptional patience and generous

help under a bombardment of questions while I was

acquiring the computing skills on which this study

depended. I would like to extend similar thanks to Adrian

Simpson for being so tolerant and helpful with statistical

advice to, John Elliott for all his help and encouragement

in the early days of the project and to Judy Doyle and

Vicki Bruce for checking the final script.

CONTENTS

Chapters

1 Introduction 1

2 Motor Behaviour Research 4

3 Bicycle Riding as an Example of Human Skill 25

4 The Computer Model 55

5 The Calibrated Bicycle 85

6 Simulation of the Destabilized Bicycle Control 119

7 Control of the Autostable Bicycle 168

8 The Biological Correlates of the Control System 198

9 The Organization of Control

References

Appendices

234

254

l(a) The Simulator Programs 260

l(b) Scale Drawing of the Destabilized Bicycle. 272

2(a) Roll and bar angles. 274

2(b) Roll and bar rates.

2(c) Histograms of lag, half-wave & area.

3(a) Effect of Gain on Stability.

3(b) Regression residuals plots.

3(c) Relation between residuals & roll angle.

281

294

300

305

312

Bicycle Riding Chapter 1

1. INTRODUCTION

Much of the research into motor behaviour starts from

some theoretical position and explores the adequacy of

this experimentally. A task is chosen either because it

offers some specific advantage in the laboratory in terms

of ease of recording the variables or because it focuses

on some detail of particular interest to the theoretical

argument. Most naturally arising skills are too complex

and loosely defined to be examined in toto. The hope is

that rules of operation will appear in the laboratory

experiments which can then be used as primitive building

blocks from which complete skills can be synthesized.

This study starts from the opposite position. It takes

a naturally arising skill and attempts to analyse it so

that a determinate system model will accurately predict

the behaviour, over time, of a selected set of variables

measured on the real machine. Bicycle riding was chosen

because its inherent unstability allows only a few

alternative strategies of operation.

The word system appears frequently in the following

text in a number of different contexts. In its normal use,

such as in nervous system it is rather loosely defined to

mean a large number of parts connected together in a

determinate way to act as a complex whole. When it applies

to the bicycle control problem I will attempt to follow

Ross Ashby's tighter definition (1952, 2/4, page 15) by

using the word to refer to that particular set of

variables chosen by the experimenter to represent some

event in the real world. Thus the changes in lean angle

and steering angle over time recorded from a bicycle

constitute a system representing that particular part of

its behaviour, although, as will be shown, this system is

too limited to be state-determined and other variables

1


must be added to form a system capable of accurate

predictions.

The first chapter is a review of the various general

theoretical approaches to skilled motor movements to which

the particular details of this study will be related in

the final chapter.

The second chapter deals with the specific control

problems that arise from the nature of the rider/bicycle

combination regarded as a mechanical system. It reviews

some of the engineering research that has been done into

the bicycle and touches on the psychological research into

feedback control loops in humans.

Chapter three describes in detail the computer

simulation of the bicycle which is used to test various

control systems for their effect on the general

characteristics of the bicycle/rider unit in later

chapters.

The next two chapters use the records from a specially

constructed bicycle to show in detail what a control

system must do to achieve slow-speed, straight-line

riding. In order to guarantee that all the control

movements of the riders were recorded and that these were

the only movements being used for control, the automatic

stability provided by the front forks of the normal

bicycle was removed to create a 'zero-stable' bicycle. It

was found that in the absence of built-in stability the

riders themselves provided sufficient for control. The

analysis shows that the principle control of roll velocity

for lateral stability was continuous but argues that there

is strong evidence that an intermittent movement

superimposed upon this underlying action was being used to

control the angle of lean. When the proposed control

solution was implemented on a simulation of the

destabilized bicycle it produced an output characteristic

almost identical with that obtained from the real riders.

2

Bicycle Riding

Chapter six

by the runs

Chapter 1

considers how the control system suggested

with the destabilized bicycle relates to

riding a normal bicycle. A comparison with an exactly

similar set of runs on an unmodified bicycle indicated

that there was little difference between the two in the

slow straight-ahead case, the automatic control being

relatively ineffective at very low speed. The general

interest in bicycle control must obviously focus on

manoeuvring at normal riding speeds and the original hope

had been to examine the effects of increased speed and

manoeuvre on both types of machine. Unfortunately, lack

of time prevented any further recording, and the only

successful record of a manoeuvring run available was one

made during the early pilot tests. The information from

this run together with some general observations of

control technique at speed and the predictions from the

computer model are used to hypothesize the most likely

technique for normal bicycle control. Once again the

predictions of the simulated bicycle using the proposed

technique show a close similarity with the output from the

real run.

The penultimate chapter discusses the requirements of

such a control system at the biological level and reviews

some of the research into human postural control to

illustrate the similarity between this and the control

used to balance the destabilized bicycle. The final

chapter relates the bicycle control revealed by the study

to the theoretical approaches discussed in the first

chapter and briefly discusses the problem of learning the

skill in the first place.

3


2. MOTOR BEHAVIOUR RESEARCH

Introduction

It is rather surprising, considering the experimental

effort that has been brought to bear on the subject over

the past twenty five years, that a more comprehensive and

detailed theory of motor skill is not available.

Before considering why this should be, and examining some

of the theories that have been offered, it is useful first

to establish the basic form of the problem to be solved.

The distinction between movement, motor behaviour and

skilled behaviour is not a rigid one. The word skilled

entails a suggestion of intent on the part of the subject

but it is evident that there are many examples of complex

predictable behaviour which the psychologist would wish to

explain, and yet where the intent of the subject for the

end state is either absent or open to question. It is

therefore better to redefine the class of movements under

investigation as predictable movements where the end state

can only be reached by virtue of the precise application

of forces generated by the subject's muscles.

The study of motor skills embraces animal activities as

widely separated as the flight of a locust (Wilson,196l)

and piano playing (Shaffer,1980). In the former case a

full explanation can be made of the actual behaviour by

showing how oscillations in the controlling neuronal cell

lead, via activity in the connecting nerves and muscles,

to effective flight. Such an explanation, however, says

nothing about the origins of this relationship, nor is

it obliged to deal with symbolic cognitive activity in

the brain of the locust. At the piano-playing end of

the scale, although we find peripheral events which seem

very similar to the locust wing movements such as the

4


lowering and raising of a digit, there are also essential

mental acts directing and modifying the action in such a

way as to preclude a description of the total behaviour in

the same simple terms.

Two major problems may be identified:-

1. How are the apparently almost limitless degrees of

freedom of the structure constrained?

2. How do complex behaviours develop?

Skilled motor behaviour always involves some

predictable goal or end-state but the exact route taken

from start to finish is seldom exactly defined.

Articulated limbs have a wide range of possible movement

and any independent change in one segment affects all the

others. For example there is a very large range of

possible trajectories for the upper and lower arm in

moving the hand from one fixed point to another. Boylls &

Greene (1984) quote Bernstein' s comment that when the

disposition of the soft tissue in relation to the rigid

skeleton is also taken into account there is an even

greater degree of freedom. Skilled movements have to

synchronize with both internal and external changes during

action and the problem is what is controlling these

changes?

The problem of development is no easier. This may be

considered on two time scales. In the first place how

does a fully mature individual develop the ability to

carry out a new skill? This cannot be viewed simply as a

matter of memory or understanding. Knowing 'how' to hit a

golf ball is not the same as being able to do so. During

acquisition, performance changes take place which must be

reflected in some physical change.

The longterm development from conception to maturity is

even more problematical. Information processing theories

5


postulate that central programs extract information about

the current physical state from the sensory input in order

to control output values to the muscles. To do this the

program must possess the knowledge about interpretation

and synchronization before the action takes place. The

problem is, how and when does the system get this

knowledge? Associated with this problem is the fact that

changes of physical scale in the skeleton and tissues

during growth require changes in the specific instructions

at the muscular level to achieve the same overall

movements (Kugler et al., 1982). Some theories see the

simple movements present at birth as primitive units which

combine later to make complex behaviour. If it is

proposed that such movements are controlled by programs of

instructions then they must alter during growth to achieve

the same movements. It is also claimed that the simple

programs present at birth modify themselves during

development to produce the mature performance (Zanone &

Hauert, 1987). The knowledge to achieve these changes must

also be present at birth, and once again the problem is

where does this knowledge come from?

The Mechanical Model

Almost all the research into motor behaviour so far

has been based on a mechanical model. In its simplest

terms this regards the skeleton as an articulated

framework which is moved by the muscles acting as

motors. When stimulated a muscle either contracts or, if

movement i~ physically prevented, produces an increase in

tension. The rate of change of contraction in the muscle

is seen as being directly controlled by the rate of change

of activity in the efferent nerves connected to it. The

afferent nerves terminate in sensory devices which,

operating as transducers, turn changes in stretch, shear

and pressure into electro-chemical activity in the nerve

6


pathways. This activity is seen as feedback giving

information about the current state to the control centre.

In general three sources of efferent change are

envisaged. First, activity in the afferent pathways from

neighbouring muscle fibres, and possibly joint receptors,

is fed more or less directly to the motor efferents to

give coordinated changes. For example, to allow movement

about a joint, the contraction of the muscle group on one

side must be matched by an inhibition of the group which

opposes it. Second, activity in a sensory afferent pathway

due to some external change is fed, again more or less

directly, to an appropriate muscle group to produce a

rapid movement. A simple example of this sort of reflex

action is the blinking response of the eyelid to a puff of

air into the eye. The third class of efferent change

comes from more remote sources in the central nervous

system (CNS) where no simple direct pathway has been

established linking it exclusively with the local afferent

system.

Before dealing with the complexities of the last class

of connections it is worth pointing out that the evidence

from nearly a century of research does not unequivocally

support the mechanical model. The neuronal pathways are

so complex and extensive that they are able to support a

great variety of schemes. Even the most straightforward

reflex loops seem to be open to modification from changes

originating at a higher level in the CNS and although the

idea of synchronous exchange of control influences within

groups of muscle fibres is well establiShed the actual

connections and method of operation is open to many

different interpretations.

The State of the Art

Motor control research is not self-contained. At its

boundaries it blends without clear distinction with

7


neighbouring areas such as cognitive science, linguistics,

artificial intelligence and neurophysiology. The body of

research can be seen as dividing approximately into the

three major classes of structure, behaviour and theory.

These are not watertight divisions as all three are

present to some degree in any research, but in most cases

it is evident that the work is more directly orientated to

one, particularly in the methodology.

Class I. Structure

Research into structure takes as its departure point a

detailed description of some local part of an animal. The

techniques are those of the neurophysiologist with an

emphasis on staining, electro-chemical probes and

micro-voltage recording techniques. Movement in the

locality of interest is explored with in-vivo and in-vitro

preparations and explanations take the form of

mathematical or electro-mechanical analogue models which

attempt to formalize the relationship between neural

activity recorded at different sites. Some of this work

has reached a very high degree of explication such as the

relation between the vestibular system and the movements

of the eye (Robinson, 1977; Boylls, 1980). It is with such

explicitly described structures that all theories of

central control must eventually interface.

Class II. Behaviour

Whiting (1980) laments that much research into motor

performance is inapplicable to observed human behaviour.

He quotes Kay as replying to the question 'What kind of

system controls human skills?' with 'one must say exactly

what we are trying to understand .... the beginning lies in

a precise description of the essential features of

skilled performance.' Researchers with this view

concentrate on those spontaneously arising accurately

8


repeatable sequences of movements which may be

unequivocally termed skilled behaviour. There are also a

much larger number of experiments which investigate simple

movements devised by the experimenter to tease out some

particular point. An example of the former is given by

Whiting's own use of the Selspot technique to record

movement overtime in games skills. Stelmach's (1980)

experiments on the spatial location of arm movements

provides a typical example of the latter. The problem

with this last class of experiments, a criticism levelled

by Whiting in his 1980 paper, is that the paradigm is

often so limited that it is hard to see how it addresses

the problem of spontaneous behaviour at all. Once again a

theory of motor behaviour must eventually be reconciled

with the complete descriptions of spontaneous behaviour.

Truly ob jecti ve observation, however, is never possible

and some sort of initial theory is needed before the

variables to be recorded can be chosen. As will be made

clear later in this study the choice of variables can be

critical to discovering the underlying mechanism in a way

which can be interfaced with the next higher level of

control in th'e hierarchy.

Class IIl. Theory

Theory, the fihal class, is something of a long-stop,

because all theories will refer at some level or other to

work already included in the two previous categories. The

particular focus in this section is on work which starts

with an attempt to give an overall framework into which

the results from experiments can be fitted. Such

comprehensive theories are obviously very useful for

pulling together the mass of somewhat isolated experiments

that inevitably mark the early stages of scientific

exploration.

9


Cognitive and Non-cognitive Theories

Stimulus-response (S-R) theory attempted to explain all

movement, including skilled human behaviour such as

speech, in the terms of the physical structures of the

body. Small movements of the reflex type were linked

together in S-R chains to form a skilled movement. The

reluctance to deal with mental acts led to a position

where all the most interesting problems were either

ignored or rendered trivial.

It was evident that, in humans at least, sensory

patterns received at one time could be stored in memory

and used later to modify responses. Because feedback for

control was central to the stimulus/response conception

there was a tendency to identify any sort of feedback as

implying this form of control. The discovery that

accurate movements could be made without afferent feedback

led Lashley (1917) to propose that the pattern of

activity in the efferent pathways controlling the muscles

was directed by a central motor program which synchronized

the output of appropriate values over time to give the

observed behaviour.

The acceptance of mental acts as an integral part of

behaviour has produced a situation where theories of

information, not related to physical structure, have to be

interfaced with that part of the structure which has been

thoroughly explored. Sometimes the interface disappears

completely when all the structure is represented in

informational terms. The main divisions in theory at

present are arguments about the role of cognitive factors

in the control of behaviour.

Central control was seen as using information from

many sources, including memories of results from previous

events, initially to form and subsequently update a

central network of programs. These could run off short

segments of movement in a motor program style. During the

1 0


movement they compared the sensory feedback with a memory

of what previous actions had produced. This knowledge of

results enabled them subsequently to achieve an improved

performance.

Schema Theories

Schema theory holds that there is a program-like source

of knowledge in the brain that can furnish the muscles

with the correct values from moment to moment to achieve

intended movements. Where information about state is

needed for success this is fed back from sensors via the

afferent nerves to the controlling authority where it is

integrated in the program. The main difficulty with this

model is that the 'freedom' of the structure leads to

prodigious demands on storage and computation.

An early proponent of this class of theories was Adams

(1971, 1976) who envisaged a local control of movement

using feedback which he called knowledge of results and a

long term memory which could be updated by this called the

perceptual trace. This was an open-loop concept where the

supplied from a values needed during a movement

central program held in the memory.

were

It had been generally

observed that there seemed to be a minimum time delay of

about 200 msecs when a subject was asked to react as

quickly as possible to some stimulus (See chapter 3 for a

fuller treatment of action latencies). It was therefore

supposed that an internal 'instruction', following the

detection of a change in the environment via the sensory

system, could not produce a response in the motor system

of less than this minimum reaction time. As a result

control of movements taking less than one reaction time

were considered as being under a form of 'ballistic'

control similar to the firing of a shell at a target.

During the actual flight no influence could be brought to

bear on the missile, but a knowledge of where it fell in

1 1


relation to the target led to a suitable correction for

the next shot. This theory attempted to explain not only

how a performance was achieved but also how it might have

been learned in the first place.

Schmidt (1976) identified a number of serious

difficulties with this model, the principal two being the

amount of storage space required to deal with the large

degree of freedom of the system, and the appearance of

novel movements. He proposed a generalized motor program

which possessed all the necessary knowledge about what

should be activated and in what sequence but had no

specific values. Schmidt proposed that sequences shorter

than one reaction time were open-loop, or ballistic, using

information supplied by a recall schema. A recognition

schema checked the consequent afferent response against

the correct one held in memory.

All versions of these two schema theories are

descriptions at the information exchange level with

virtually no explicit reference to structure,

consequently they have almost unlimited freedom to chose

alternative algorithmic paths between end points. It is

difficult enough to see exactly how the neural structure

at the muscles might produce the required movements but

how the known structure of the brain might interpret

sensory inputs in order to produce the output signals

demanded by such central 'programs' is so far a complete

mystery. Such models can only be rigorously tested by

linking them via specific values to the inputs and outputs

identified in some physical event, and even then, since

they do not deal with specific structures, they can tell

us nothing concrete about structural development. In

general neither of these models, nOr their many derivative

versions, pay sufficient attention to the fact that there

are many motor movements which show close coupling with

the changes in the environment at less than 200 msecs

12


Quite apart from the difficulty of identifying

appropriate interface values, the information-flow model

of control suffers from another serious inadequacy. The

model handles the logical flow of information from input

to output but in itself it has no knowledge about this

information. The knowledge about the sequence of events

and what the values in the program represent is supplied

by the programmer. Also the relationship between that

knowledge and the representing values is arbitrary. If a

central program-like operation in the brain 'knows' that a

certain rate of activity in a nerve coming from a

particular senSOr must be fed at a modified rate of

activity to a certain muscle at some exact time then HOW

does it know this? The modelling program knows it because

the experimehter already has a personal mental model of

the whole situation which supplies this knowledge. The

objection to this sort of explanation is that it leads to

an infinite regress with respect to the origin of the

knowledge needed to drive it, an objection which Bernstein

characterizes as making 'borrowings from the bank of

intelligence .... loans which it has no means of repaying'

(Kugler et al., 1982).

Despite these difficulties there can be no doubt

that, providing the input and output interfaces do

actually lie somewhere within the physical structure, the

computer analogy is an important and powerful tool for

imposing order on what happens between them. The further

towards the periphery of action the model extends the less

it explains as the problem of selecting the one desired

path from amongst so many is referred back to the unknown

source of initial knowledge. The success of such an

enterprise depends on establishing an hierarchy of

semi-autonomous levels of function which serve to reduce

the degrees of freedom by placing constraints at the local

level. Perhaps the real value of this approach is that

13


once a theory has been developed as a running program it

is possible to identify the penalties, in information

handling terms, of the proposed algorithms.

The Return of Non-Cognitive Theory

Despite the dominance of cognitive central control

theories there have been voices crying in the wilderness.

Perception is the act of transforming sensory inputs from

the external world into the knowledge base on which

central control theory depends. Gibson (1950) not only

objected to the combinatorial implications of a

knowledge-based central control for locomotion, but

produced the groundwork for a viable alternative which has

gradually been taken up by an increasing number of

workers. The main thrust of his position is that the

visual system does not extract dimensional information

such as angles and distances but non-dimensional values

which can be used to control movement directly without the

intervention of insubstantial mental percepts. Lee (1974 &

1980) subsequently developed equations for properties of

the two-dimensional projections on the retina during

movement which yielded such non-dimensional invariants as

time-to-impact to or course for cOllision with a location.

He showed that this could be derived from the velocity of

the image with a dramatically lower order of processing

than that demanded by even the simplest system for

extracting knowledge. In addition it had virtually zero

storage demands. Not only does such a finding posit a

system which dramatically reduces the degrees of freedom

at a low level in the control hierarchy but it also

suggests that the traditional way of looking at the

problem might be making it seem harder than it really is.

Another example is provided by the operation of the arm

muscles to produce an accurate pointing movement. To

control each muscle independently from a central program

14


requires a great deal of information feedback about the

progress of events at the periphery. There are endless

combinations of limb positions possible between the

initial and final positions defining a movement and each

one will require a different sequence of control

instructions. Computer programs can solve this sort of

problem but in order to do so for complex movements they

need prOdigious amounts of storage space, very fast

processing and a good deal of specific knowledge.

Recently it has been proposed (Stelmach & Requin, 1980

p.49) that these two muscle groups operate together as a

unit with properties similar to those of a linear

mass-spring system. This requires a completely different

input from the central control as a single length/tension

ratio for flexor/tensor muscles regarded as a unit will

specify a unique position in their plane of movement. Thus

the central programs associated with these two different

types of input will also be completely different. In the

latter system the control problem is much simpler as the

program can use the ratio as a primitive in combined

movements without any of the previous overheads, its

output specification being simply a destination regardless

of the present state. In going to the new position the

system may pass through a wide variety of trajectories,

depending on where it started and what external conditions

it experiences on the way, but this freedom does not alter

the fact that it is uniquely constrained as to its end

state by the single input value. (Kelso et al., 1980;

Bizzi, 1980; Cooke, 1980).

In the above model the degrees of freedom are reduced

at a low level in the hierarchy by a semi-autonomous local

system which contains its 'knowledge' in the structure,

leaving much less to be accomplished by the central

control. There is a double disadvantage of leaving too

much to a computer-like central program. On the one hand

15


we cannot say from where it gets its knowledge and on the

other, since the theory does not address the problem of

what physical structure supports the program, nothing

is said about its development either. When the advantages

of a semi-autonomous hierarchical system are considered it

is difficult to imagine anyone wishing to continue with

any theory of non-hierarchical central control.

Recently a theory has been proposed which considers the

structure of animals as acting like a thermodynamic engine

in a state of non-equilibrium rather than as a mechanical

engine. This view promises to have far-reaching effects

on the whole theory of motor behaviour and is sufficiently

new to warrant a longer exposition.

The Theory o'f Naturally Developing Systems

The mechanical analogy described in the previous

sections forces the view that each unit of the system,

such as a single muscle fibre, is controlled for change of

position over time by the incoming nerve impulse which

takes its value from some central controlling system. The

integration of the behaviour of this unit with that of

other units is achieved at the control location which

further forces the view that information about the

system's state must be fed back to the central control as

well. All research into motor behaviour is either directly

or indirectly

problem.

related to the solution of this control

Two main difficulties become apparent. First as the

nerve pathways are traced back into the CNS the number of

autonomous or semi-autonomous units becomes so great that

it is increasingly difficult to isolate individual

transmissions. The generality of involvement in the brain

itself led to the idea of mass action initially proposed

by Lashley (1929). This was not a theory in itself so much

as an abandonment of the mechanical analogy. The second

16


problem is that, although animals can show great preCision

in their ability to move a limb from one point in space to

another the number of possible pathways which can achieve

this are very large. The problem is how this very

extensive freedom of choice is limited by the control

system.

Kugler, Kelso and Turvey (1980) have put forward a

new theory of naturally developing systems. This theory,

further elaborated in later references (Kugler et al.,

1982;1984), claims to draw principles from philosophy,

biology, engineering science, non-equilibrium

thermodynamics and the ecological approach to perception

and action. The main thrust of their argument is that

animal movement should be treated not as a mechanical

but as a thermodynamic engine. The essential difference

bet~een these twb systems is that in the latter a very

large number of semi-autonomous units interact with each

other, remote frdm any central control, in such a way that

the statistical sum of their movements leads to a stable

state at a higher level of organization. For ease of

reference the idea of two associated states at different

lev~ls of organi~ation will be termed micro and macro.

Certain non-dimensional variables in the system, labelled

'essential' variables, are identified as having a

controlling effect on this transition between states. When

the essential variable is between two limiting values the

system as a whole goes into a stable macrostate.

The Benard 'convection instability' phenomenon is

given as a simple physical example of this sort of

system. If a tank of fluid is heated from below but kept

at the same temperature above, the heat is transported to

the upper layers by conduction only, providing the

temperature gradient is smaller than some fixed limit.

When the gradient exceeds this critical value the

organization of the fluid undergoes a radical alteration.

17


Large groups of molecules coalesce, breaking away from the

lower layers

Despite the

to rise in a pattern of convection currents.

freedom of the structure at the molecular

level, the macrolevel is first in a stationary homogeneous

state and then changes to one of well-ordered movement. A

third state in which the convection patterns become

oscillatory is reached if the gradient is increased beyond

a second critical value. In this system the essential

variable is the temperature gradient and changes here

force the system into different locally stable states at

the macrolevel of description. Nonessential variables such

as the tank dimensions or externally introduced flow rates

will alter the details of the rising convection patterns

but will not change the stability condition.

Seen in this light the ordered behaviour of a

biological system between two limit values of its

essential variables is the same order of event as the

volume, temperature and pressure states of gases as a

result of the molecular activity at the microlevel. We are

unable to argue to the macrostate from a knowledge of

events at the micrcilevel. In fact nuclear physics

declares that the appropriate macro quantities of position

and velocity no longer mutually exist at the lower level.

What we do in the case of the gas laws is accept that,

however it may be done, the relationship between the three

values is fixed as long as the essential variables are

between the relevant critical values. Beyond this limit

the gas liquefies

relationships appear.

or solidifies and different

The reason we believe this is not

because we can argue it logically from some other position

but because it is always observed to be true. The

essential difference between the physical and the

biological cases at present is that we have not yet

devised a dimension of measurement for the latter which

reveals similar invariant laws.

18


One of the most important consequences of this view is

that the order observed in the system at the macrolevel is

an a posteriori fact resulting from the nature of the

myriad interactions at the microlevel. No conception of

what this order might be need exist prior to the

realization of the state which produces it. This is a

very telling point because it is evident that any attempt

to describe the same process at the macrolevel in

computer program or cybernetic feedback control terms

requires specific a priori knowledge of the future steady

state. Once such a description is offered as a theory of

behaviour it begs the question 'where does the a priori

knowledge come from?' The advantage of describing the

events in terms of a thermodynamic engine is that no such

prior knowledge is required. The emerging state of order

is the inevitable consequence of the microscopic

structure. Thus, at a blow, two of the most intractable

problems of control are by-passed. First the

number of degrees of freedom associated

very large

with the

individual muscle fibres is no longer a problem because it

is the very number that allow the statistical nature of

their integration. Second since the relationship between

microactivity and macrostate is embodied in the structure

there is no need to postulate a controlling program and

therefore the problem of where that program gets its

knowledge also disappears.

Kugler et al. give details of a number of theories

which deal with this relationship between structure and

function, the two most important being 'Dissipative

Structure Theory' and 'Homeokinetic Theory'. Although

these two theories take different views in detail they

agree in describing how a thermodynamic system may pass,

at some macrolevel of description, in sudden steps through

states of local equilibrium which exist by virtue of the

complex interaction of many independent units at the

19


microlevel. Systems of this sort are not closed and

therefore do not obey the laws of equilibrium

thermodynamics. Consequently they do not have to move

always towards a state of maximum stability and chaos but

by virtue of being open and having access to some external

source of energy they can move to locally stable

states of greater complexity and order. Furthermore it is

the nature of non-equilibrium thermodynamics that systems

tend to make such moves as sudden 'catastrophic' jumps to

positions of local equilibrium which they maintain until

the essential variables alter to a new critical value.

Thus it can be seen that such a system can show

development from a less organized to a more organized

state, in a more or less short term jump, providing the

'essential' variables force it to do so. For example in

relating such a system to the case of change of limb

movemerits with age in the growing child, the essential

variables would be seen as the length and weight of the

skeleton and muscles, and the change in movement patterns

would be the necessary consequence of the previous

microactivity working at the new macrostable level.

This new theoretical approach of Kugler, Kelso and

Turvey is very promising and serves as a reminder the

relation~hip bet keen the mechanical engine analogy and

motor nehaviour is still very tentative. Information

theory ahd cybernetic theory are attractive because they

offer ways of organising a wide range of observations in a

form which allows discussion and promises a way into the

problem. The Dissipative structure offers another way and

makes different but equally interesting promises about its

possible power. As the authors themselves agree (Kelso,

1980, pp 65-66) there are as yet no conclusive experiments

to show that biological structures are organized as

dissipative systems, but neither are there any to show

that mental acts are organized along the lines of

20


information theory. The latter runs into a major

difficulty in that it says nothing about how the knowledge

necessary for its operation becomes available at the

natural level, whereas the former specifies that

'knowledge' is a by-product of man's mental model of the

situation and that the function of the biological

structure itself is completely specified by the way it is

put together.

One weakness of

ignores the fact

exhibit symbolic

the Kugler

that AT

et al. approach is that it

SOME LEVEL humans do

mental behaviour. This thesis is an

example of symbolic activity only arbitrarily and remotely

linked with the supporting biological structure. It is

also evident that mental acts at this level can be very

rapidly translated into specific physical acts.

Consequently any theory of human behaviour must take

account of the need for an interface between these two

different forms of behaviour. Although the authors do not

mention specifically that even abstract thought might be

seen as the inevitable consequence of the physical

structure of

ecostructure

the brain

it looms

in

in

relation to the

the background as

surrounding

a logical

extens ion of the basic idea. It is evident that even a

hint of such a deterministic solution would be sufficient

to alienate many workers in the human behaviour field

(Zanone & Hauert, 1987). However even when fears of

predestination and biochemical automata are set aside the

model carries with it the disadvantage that the details of

the link between the micro structure and the macro

behaviour are seen as opaque and it therefore has less

potential as a predictive theory.

Applying the Thermodynamic Engine Theory

It is fairly obvious that man's mental models of an

external reality will never capture the detail on every

21


dimension. A model is in effect a simplifying tool for

making serviceable predictions at the level of interest

despite lack of precise knowledge at some more complex

level. Good predictions are usually associated with

specialization and the more specialized the model the less

well will it map onto other specialized models. For

example a map which allows compass

represented as straight lines will have

bearings to be

to distort other

aspects such as area. No single two-dimensional map can

faithfully represent all the surface features of the globe

because there is a dimension missing. Scientific

theories, like maps, are models for making useful

predictions about future events from limited data.

Therefore in considering theories of behaviour we

should not be too upset if we find that a theory which

makes good predictions about mental acts does not map

directly onto a theory which makes good predictions about

physical movements. The Dissipative Structure theory

promises good power in explaining the sort of behaviour

that is not much influenced by cognitive operations. In

fact since the theory makes no allowance for such

interferences it might serve as a defining test for

behaviours that are not so influenced. Where it is

evident that cognitive activity is making a significant

contribution to behaviour then the interface between the

two systems becomes important.

Kugler et al. (1982, page 45) reject dualist theories

which posit causes and effects between the environment,

described in physical terms, and percepts, described in

mental terms said to be 'in' the animal. Their objection

is that the interface between these two regimes is

arbitrary, whereas their view shows that the emerging

order in the natural event is a by-product not a

controlling cause. However the point is that, at the

present state of the art, there is no chance at all of

22


describing the sort of dissipative structures that might

support existing cognitive abilities as an a posteriori

by-product. In fact it is only a few short years since

information and computer theory have allowed us to get a

systematic grip on cognitive activities. However

unsatisfactory the arbitrary interface between mental

events and physical acts might be, it does exist. It is

itself a by-product of our investigative tools and like

the two-dimensional maps that will not quite fit together

we must accept, for the present at least, this

discontinuity if we wish to keep the power of the separate

tools intact. Too much concern about exact mapping of one

theory onto the other will merely lead in the direction of

a futile attempt to build a model that is as complicated

as the world it is meant to simplify.

The task facing the proponents of the dissipative

structure theory is first to show that the internal logic

is sound, as has already been shown for information

theory, computer theory and cybernetics, and second how it

may be applied experimentally. Like the gas laws, the

theory does not expect to show how the activity at the

micro-level leads to changes at the macro-level in detail.

Consequently its power will lie in its ability to find

invariant laws which operate at the latter level and

identify the 'essential' variables which control them. A

description of the biomechanical aspect of motor behaviour

in these terms would certainly ease the interface problem

but so far it is but a promise.

Summary

This chapter has discussed the current theoretical

approaches to the problems of motor behaviour. The next

chapter will introduce bicycle riding as an example of a

skilled motor behaviour in which the freedom of movement

of both the rider and the machine is severely constrained

23


by the inherent instability. Subsequent chapters will show

how this constraint allows a detailed record of the

movement of the machine during free riding to specify what

the rider must be doing to achieve it. The structural

correlates needed to implement this control behaviour will

be discussed before relating it to the theories introduced

in this chapter.

24


3. BICYCLE RIDING AS AN EXAMPLE OF HUMAN SKILL

Choice of Skill

Bicyle riding is a very common skill found in all the

civilised and semi-civilised parts of the world. It is

usually learned at an early age and it must be supposed

that most of this learning takes place without any formal

instruction. It is principally a problem of delicate

balance and the fact that it must be learned is an

indication that although it may depend on the same basic

structures as standing and walking the skill does not

transfer automatically. There are two indications that it

is very close to existing balance skills. First it is

learned quickly; A confident and enthusiastic child will

learn the rudiments in a day or two which represents only

a few hours of actual practice. This can be compared to

the skills associated with musical instruments where a

year or more may be needed to acquire a good tone on a

violin or an oboe. Second it is well learned. The old saw

says that 'Once learned, never forgotten' and this again

contrasts with musical skills which are usually lost after

quite short periods with no practice.

It is possible to learn a certain amount about bicycle

control from straightforward observations. By operating

the handle bars with various parts of the lower forearms

it is possible to glean that the skill does not depend on

the sensory input at the hand's surface. In the same way a

variety of extreme body positions such as standing on one

pedal and leaning away from the machine, or leaning right

over the front wheel seems to have little effect on

control. Many riders can keep quite good control without

holding onto the handle bars at all although some bicycles

will not allow this form of riding. Very short or very

long handle bars seem to make no difference but reversing

the hands so the left is on the right bar and vice versa

25


immediately produces a very strong disruption and if the

steering is locked solid riding becomes completely

impossible.

If we look at the tracks left on a dry surface by wet

tyres, we see that the rear wheel leaves a gently weaving

line while the front wheel traces a sinusoidal path with a

higher frequency that oscillates either side of the rear

track or near to it. If we enter a turn quickly at some

marked position we can see that the front wheel turns

momentarily away from the desired direction before making

the turn and that this deviation does not appear in the

rear track. In a steep turn the front wheel track is

outside or at a greater diameter than that of the rear

wheel. Without some method of recording simultaneous

events it almost impossible to locate the relative

positions in time of those events recorded on the surface

with the changes in lean angle observed during the turn.

Bicycle riding shares an interesting feature with many

movement skills. Although people can do it perfectly well

they have no clear idea what it is they are doing. A

survey of ten regular bicycle riders showed 9 of them

claiming that a turn was initiated by rotating the handle

bars in the direction they wanted to go. Six of these

thought that they leaned in the direction they wanted to

go at about the same time and three thought they did not

lean. One person thought he leaned in the direction he

wanted to go but did not turn the handle bars. As will be

made quite clear in the following chapters a turn is

initiated or increased by moving the handle bars in the

opposite direction to the turn and that moving them in the

same direction will contain or reverse it. Of course it is

possible to initiate or increase a turn by failing to

produce sufficient handle bar to contain the fall rather

than actually turning the bar in the reverse direction but

a simple study of wet tyre marks on a dry surface

26


immediately reveals that the normal practise is to

initiate a turn with a short reversal of the bar, even

though it is evident that most riders are quite unaware of

this. Richard Ballantine, author of the popular vade me

cum, Richard's Bicycle Book (Ballantine, 1983),

specifically mentions turning the bar in the wrong

direction as a special way of entering a turn quickly but

otherwise seems unaware that this is the normal way as

well. Ross Ashby (1952) states quite clearly

the handle bar

in his

must be Design for a Brain not only

initially be pushed in the

that

opposite direction to the

desired turn but also he remarks on the fact that even

very experienced bicycle riders are rarely conscious of

this despite having carried out the act thousands of

times.

At high speed on a bicycle or a motor-bicycle it can

be easily demonstrated that a steady push tending to turn

the handle bars to the right produces a turn to the left

and vice versa. As soon as the rider and bicycle start to

fall to the left out of the initial turn the autostability

forces twist the front wheel powerfully left to check it.

Even when this is well understood it is very difficult not

to attribute the large handle bar movement into the fall

to the rider initiating the turn rather than the

autostablity following the fall. In chapter 7 it will be

shown that as soon as the push 'in the wrong direction' is

released the autostability forces stop the turn and

restore the bicycle to upright running. As for the

underlying responses to the change in roll which

guarantees lateral balance when autostability is low,

these seem to remain quite opaque to the conscious mind

even when its presence is thoroughly understood. The

situation is similar to that found by Lishman & Lee (1973)

when, in their swinging room experiments, they found that

knowing that the visual movements were false did not

27


enable them to percei ve them as such. 'Finally we

oursel ves are still visually dominated despite having

intimate knowledge of the apparatus and being subjects for

many hours. '

Essential Characteristics of The Bicycle

A bicycle is stable fore and aft, unstable from side to

side (Roll) and has a complex directional stability

depending on conditions of front wheel angle and roll

angle. When stationary a riderless bike will rapidly

diverge in roll under the influence of gravity but when

moving faster than some minimum speed it will

automatically limit this rate of divergence. Depending on

the design of the bicycle there may be some higher speed

beyond which the machine will not fall at all but will

maintain straight ahead upright running. Of course in the

absence of some means of sustaining this speed, such as a

motor or running down a hill the bicycle will eventually

slow down into the lower speed range. Turning the front

wheel at an angle to its direction of travel produces a

sideways force at the front tyre/road contact point and

this by swinging the front of the frame leads in turn to a

similar angle and force at the rear wheel. The effect of

these two forces cannot be determined by a casual

intuitive inspection of the resulting overall behaviour.

This is due to the fact that as soon as the frame angle

responds to the front wheel change the angle between the

direction of travel and both wheels is immediately altered

giving interactive changes of both rotational and turning

forces. The combination of these two forces also produces

a couple about the centre of mass in the mid-frontal (or

coronal) plane which tries to roll the machine out of the

turn and this couple can be balanced by leaning the bike

into the turn (see figure 3.1). The essential feature of

control is the management of the position of the centre of

28


gravity in relation to the wheel contact points via the

front wheel angle so that the two couples balance for

lateral stability.

The Control Model

The ultimate aim of this study is to shed some light on

the contribution which humans make to the control of

bicycles. At this stage in the investigation, however, it

is not clear exactly was is happening let alone who or

what is causing it. At the level of action being

investigated, it will be assumed that the functioning

units controlling the rider's movements behave in a

determinate way, that is the effect of similar external

conditions on a particular internal state will always lead

to the same behaviour, and that as a consequence both the

bicycle and the human, for the purpose of analysis, may

be considered as a 'machine'. Thus the bicycle on its own

may be referred to as a system, or the combination of

rider and bicycle whet'e the former is producing one of the

variables such as the rate of handle bar movement. When

the system is spoken of as having a problem this is to

indicate that a specific relationship over time between

the variables chosen

observed performance,

provided by the rider,

is necessary to account for the

regardless as to whether it is

the design of the machine or a

combination of the two together.

The problem of bicycle control is to sense the change

in the roll angle and use the front wheel angle to control

this to a desired value. Merely reducing the rate of roll

is simple but as soon as it is reversed an uncontrolled

acceleration in the opposite direction can only be avoided

in one of two ways. Either the exact rate of steering

angle change required for that bike, at that speed, in

those road conditions at that specific lean angle must be

available to the system or it must apply some general

29


procedure which will cover all norma lly encountered

conditions. The latter solution is greatly to be

preferred both on the grounds of parsimony and because of

the difficulty of finding physiological structures to

account for the sensing of some of the values required by

the former. Also the output characteristic of each is

different, the former giving a 'dead-beat' performance

where changes in angle are stopped exactly at the target

value whereas the latter always overshoots to some degree

and shows regular fugoid divergences either side of the

target, which, as will be shown later, is one of the

identifying characteristics of human bicycle control.

There are usually quite a large number of different

control arrangements which will produce similar

performances from the same machine. One of the major

advantages of bicycle riding as an experimental example of

a skill is that the extreme instability in roll allows

only a very limited number of

making identification of

possible control solutions

the one actually used

considerably easier than it would be with a more stable

one.

Existing Studies of Bicycle Riding

The single-track vehicle is a very complex dynamic

machine which is not easily reduced to manageable

mathematical representations. There do not seem to be

substantial commercial rewards for marginal improvements

in a device which is already extremely successful as a

cheap personal transport, which probably explains the

comparatively small amount of research in this area. weir

and Zellner (1979) claim a comprehensive bibliography of

21 papers and of these only four deal specifically with

the rider's contribution to control. In these latter

papers the authors compare the performance of mathematical

models of the motor-cycle rider/machine system with

30


records of riding behaviour. Their main concern is to

improve the handling performance of the vehicle and the

human contribution is seen as an essential but secondary

consideration. Both Weir and Zellner (1979) and Eaton

(1979) considered that basic balance control was achieved

through a simple delay repeat of the roll activity as a

handle-bar torque force or upper body displacement. Eaton

found that the latter seemed to contribute very little

during actual experiments and subsequently immobilized the

upper body of his subjects in a frame. Weir and Zellner

provide models for both combined body and bar movement and

bar movements alone. Neither seems to have considered that

the powerful gyroscopic effect of the front-wheel design

in motor-cycles converts lateral body displacements to

front wheel steering movements, so that upper body

movement may just be an

handle-bar control. A study

alternative option to

by Nagai (1983) also

considers these two forms of control without mentioning

the automatic interaction between them in normally

designed machines. The distinction is not very important

from their point of view but is of prime interest as far

as a study of rider skill is concerned. An investigation

by Van Lunteran & Stassen (1967) used a static

electro-dynamic bicycle model that ignored the

contribution of centripetal forces altogether thus

fundamentally changing the skill required to achieve

balance.

Jones (1970) attempted to penetrate the mysteries of

bicycle mechanics by constructing an unridable bicycle by

systematically removing those features which were supposed

to confer stablity. Despite a rather lighthearted

treatment Jones' paper has been much quoted since and

therefore deserves a slightly longer treatment. This

however will be postponed until some aspects of bicycle

design have been covered.

31


BASIC CONTROL

Bicycle riding has three basic requirements. These are

hierarchical, that is A is necessary for the performance

of Band B is necessary for the performance of C.

A. Don't fall over.

B. Turn where and when you want to.

C. Avoid obstacles and go to desired places.

This study is only concerned with the two lower levels

of the hierarchy and aims to find out exactly what happens

in the combined rider/bicycle machine between the top

level instructions GO-LEFT/GO-RIGHT/GO-STRAIGHT and the

resulting performance. In a way it can be regarded as a

navigation task on top of a steering task on top of a

postural task. However, as will be made quite clear, the

demands of the former must be met on the terms dictated by

the latter.

The simplest possible control would be to treat the

handle bar as though the bicycle was a tricycle. When the

request GO-LEFT is given the bar is moved left. The

response to such a movement is a violent fall to the

right. Some idea of the forces involved can be gained

from the way a motorcycle combination will lift the full

weight or its sidecar plus passenger off the road in quite

a moderate turn towards the car. It can be seen that this

at least is not a candidate for the control of an

unsupported bicycle. The control problem in general terms

is that although directional response can be achieved

using the bar like a car steering wheel it will lead to

instant loss of roll stability. In order to find

solutions to this problem further analysis is needed.

There are two major influences on the roll stability,

the couple due to the weight and the couple due to the

turn. Figure 3.1 (b) shows how the weight acts about the

32


horizontal distance 'd' between the centre-of-mass and the

support-point of the tyres to produce a rotating couple 'W

x d' in the rolling plane.

couple

Wxh

h

(a)

Figure 3. 1 The turn and lean couples.

(a) Turn force gives a roll out of the turn.

(b) Off-centre weight gives a roll into the lean..

(c) The turn and weight couples cancel each other out and lead to stability in roll.

couple

\Wxd

'-- .. -'

d

(b)

h

The greater the angle of lean the greater the rotating

couple for any given weight. This is a sine relationship

so the rate of change is small at first but gets rapidly

bigger beyond 45 degrees. Since people can ride bicycles

at an angle without falling over it must be possible to

balance this with some other couple. There must always be

a force present acting towards the centre of any turn,

usually termed the centripetal force. On a bicycle this

force comes from the strong sideways component of drag

33


generated when the tyre runs at a slight angle to the

direction of travel. Figure 3.1 (a) shows how this force

at the tyre/road contact point produces a couple 'F x

h' by acting over the vertical distance 'h' between the

centre of mass and the ground. This couple is a cosine

relationship and is at its greatest for a given force

when the bike is vertical and gets rapidly less beyond 45

degrees lean.

Imbalance of Couples

It can be seen from the foregoing paragraphs that

providing the bicycle is leaning into the turn the weight

couple opposes the turn force couple. However it can also

be seen that they are not well matched since the former

gets bigger with increasing lean angle whereas the latter

gets less. It is this mismatch that is at the heart of the

bicyle control problem. Figure 3.2 illustrates the problem

situations. In the first diagram, named 'The Fall', the

distance 'd' is big so the weight forms a very large

couple into the lean, but because of the exaggerated lean

'h' is small, so a very big force F would be needed to

check the fall. It must be borne in mind that not only

does this force have to match the couple formed by the

weight times the distance from the support-point (W * d)

but it must exceed it. Matching it will merely prevent

there being any further acceleration in roll but the

accumulated angular velocity, due to its having fallen

from wherever it started, must also be dissipated or it

will go on falling at that rate. During the time taken to

overcome the residual velocity the angle of lean will have

continued to increase so the imbalance situation will have

got even worse. The second figure, named 'The Recovery',

shows another problem area. Assume that the large increase

in Force has successfully contained the fall and the

machine starts to return to the upright. At first the

return will be moderate as the couples are well matched

34


but as the angle reduces the roles will be reversed and

the rapidly increasing 'hid' ratio produces a much bigger

restoring couple than the disturbing one and the roll

velocity becomes excessive so that when the machine passes

the vertical and starts to fall the other way the recovery

problem will be even greater than before. It can thus be

seen that if the roll rate is to be controlled there must

be a continuous and finely balanced relationship between

the Weight and Turn Force couples.

F

~ I ~ d ~

h

lh W

J W F

The Fall The Recovery Figure 3.2 The two problem situations in balancing the disturbing and correcting couples. In the Fall the couple Wxd is very big and since 'hi is small then F must be very big to produce a correcting couple. In the Recovery the height 'hi is now big and Id' is small. If the wheel force F is still big then the restoring couple Fxh is much bigger than the destabilising couple Wxd.

To achieve the minimum control requirement 'Do not

fall over', it is necessary to use the unwanted rate of

roll as the actuating signal which will drive the system

so that roll rate is removed. Movement in roll may be

considered as having two components, angular acceleration

and angular velocity. The resultant of the weight and turn

couples produces a change in acceleration and this, acting

over time, changes the velocity.

The control exercises its influence through changes in

the front wheel steering angle which in turn controls the

35


side force at the tyre/road contact point, which in turn

alters the turn couple. It has already been mentioned that

merely reducing the acceleration to zero by balancing the

roll couples is insufficient as it leaves the accumulated

velocity unaccounted for. For a minimum solution the

control must produce changes in the sideways wheel force

via the steering angle that are dependent on both the

acceleration and velocity in angular roll. This will

remove any roll movement that arises giving a constant

lean angle. Where this angle is other than vertical the

bicycle will be turning towards the lean.

Autocontrol

Over the years the front forks of the bicycle have

evolved to a specialised form that provides a considerable

degree of automatic directional and roll stability. Figure

3.3 shows four different front fork arrangements. In the

first the hinge line is vertical and there is no offset of

the front axle. The contact point of the tyre with the

road is directly in the hinge line. In this configuration

any force applied at either the contact point or at the

frame/hinge junction cannot form a couple and will

therefore have no influence on the steering angle.

In the second view the axle has been offset to the rear

forming the trailing castor arrangement familiar in the

wheels of movable furniture. Here any sideways force at

the road contact point will form a couple over the

distance marked Trl and drive the wheel steering angle

back towards zero, thus damping out the effect. Any side

force at the frame/hinge joint will also act over this

distance so that when the bike is leaning to the left,

say, the weight of the machine and rider will give a force

to the left which will produce a couple rotating the wheel

into the direction of lean. Since this will make the

machine turn to the left, which will in turn produce an

36


anti-lean couple, it is a stabilising movement in the roll

plane.

(a) No rake & no offset, (b) No rake but rearward therefore no castor. offset gives castor.

(c) Rearward rake, no offset (d) Offset axle reduces gives a large castor. the castor effect.

Figure 3.3 Showing how variation in the geometry of the front forks gives different trail distances and thus different castor effects.

When the safety bicycle replaced the ordinary or

'penny-farthing' type the rearward movement of the rider

necessitated a rearward movement of the control bar. This

was almost universally accomplished by raking the hinge

line back at an angle. Such an arrangement is seen in the

third diagram. As can be seen the effect of such a design

is a large distance between the ground-tyre contact point

and the hinge line. (Marked Trl). This gives a powerful

stabilising effect which makes it difficult to turn the

wheel out of the dead ahead when upright and produces such

37


a strong couple into the lean when tilted that, if

allowed to dominate, it leads to overcompensation and a

series of wobbles from one side to the other. This is not

a desirable state of affairs for normal control and the

'stability' factor is reduced by offsetting the axle

forward to reduce the distance Trl. This dimension is

adjusted to give sufficient directional stability to

prevent stray bumps jerking the steering into dangerously

excessive angles and some

steering in the direction of

volitional movements by the

assistance in turning the

roll changes without opposing

rider. This configuration is

shown in the final diagram of fig. 3.3.

Gyroscopic Effect

FI •

R2~ F2"-!!If

n RI

Figure 3.4 Showing precessional effect on a wheel acting as a gyroscope. A force applied at FIr tending to rotate the carriage in direction RI, will act as though it was applied at F2, ie at 90 degrees in the direction of rotation. The resulting yawing movement, R2, will be proportional to the angular velocity of RI, the moment of inertia of the wheel and its rate of rotation.

When a bicycle wheel rotates it acquires the

properties of a gyroscope. When a couple is applied that

38


tends to turn the wheel axle in one of the two planes at

right angles to the plane of rotation, the precessional

effect causes a turning movement in the other plane as

though the force had been applied at a point at ninety

degrees in the direction of rotation. This is shown in

fig. 3.4. The result is that any roll velocity leads to a

stabilising movement of the front wheel in the direction

of roll. The greater the mass at the periphery of the

wheel and the faster the road speed the greater is this

effect. In a small wheel bicycle at walking speeds the

effect is very slight whereas in a motorcycle travelling

at normal road speeds the effect is very powerful.

Independent and Combined Control

The autocontrol features due to front fork design

and gyroscopic effect described above provide a couple

about the steering axis. A rider who moves the steering

bar independently of this effect will feel the resultant

couple as a resistance. In a light bicycle travelling at

low speeds the effect is scarcely detectable .. At a good

road speed, say fifteen miles an hour the effect on a

normal bicycle is marked, giving a feeling of

'inevitability' to the roll stability. Removing the hands

altogether has no immediate effect. At normal road speeds

on a motorcycle the forces are so high that only a

determined effort on the part of the rider could override

the steering head couple. Thus it can be seen that two

kinds of control must be considered for bicycle control.

Whenever the steering head couple is weak the rider must

provide all the movement necessary for stable control.

When, due to front wheel size and road speed, the

machine provides a significant level of stability control

the rider need supply only those control forces required

to alter the angle of turn in the desired direction. In

doing this the rider must not apply angle dependent forces

39


on the handle bar as these will interfere with the

automatic couples and autostability will be lost. What the

rider must do is to contribute a further couple which will

balance with the machine contributions to produce a

resultant which gives the desired effect. The important

point is that this couple MUST BE POSITION INDEPENDENT.

This means that the arms must move with the bar as it

alters its angle under the influence of the autocontrol

but at the same time provide a steady push in the desired

direction. In other words the force at the bar must be

independent of the steering angle. At the anatomical

level this means the rider is controlling the steering

muscles for tension independent of length. At the

experimental level it means that any record of changes in

the steering angle will contain contributions from both

the rider and the autostable effect of the front fork

design in a proportion which depends up such factors as

speed and individual design. Both the gyroscopic and

castor autostability must be removed from the experimental

bicycle if the record of handle-bar movement is to be an

unadulterated version of what the human operator is doing

but the description of how this is done will be left until

chapter 5.

The Unridable Bicycle

Before going on to consider the case of body movements

as a means of control Jones 1970 paper will be considered

in more detail now that the basic mechanics of the bicycle

have been explained. Since Jones' thesis was that a

bicycle without autostability would prove unridable it can

be inferred that he regarded the human contribution to be

of little importance. He used two tests to determine the

unridablity of the bicycles he built. One was to try and

make them travel on their own after being pushed off at a

run and the other was a subjective account of how

40


difficult he found them to ride. The actual words he used

to describe the result of these latter test appear below

in italics. The first unridable bicycle (URB1) had a

second front wheel mounted alongside the first, just clear

of the ground, so it could be spun up to speed by hand

either in the same direction as the normal front wheel or

opposite to it. When it was spinning in the same direction

it enhanced the gyroscopic effect and when in opposition

it diminished or reversed it. He confessed himself puzzled

when the bicycle proved quite easy to ride at low speed in

either condition. However the effect on the bicycle

running on its own was quite clear. When the gyroscopic

force was reduced the machine fell to the ground as soon

as it was released and when the force was enhanced URBl

ran uncannily in a slow, sedate circle before bowing to

the inevitable collapse (page 36). URB2 had a 1 inch

furniture castor fitted instead of the front wheel.

Despite problems with bumps and the bearing overheating

Jones was able to ride this strange machine but was not

surprised that it would not run on its own. URB3 had the

normal front forks reversed, similar to the diagram in

figure 3.3 (b). This machine was amazingly stable on its

own, not only limiting the rate of fall but actually

righting itself and turning in the opposite direction. But

it was strangely awkward to ride, because it was too

stable and resisted control inputs from the rider.

Finally in URB4 Jones exaggerated the foreward curve of

the front forks by mounting the wheel on 4 inch extension

pieces producing a strong reverse castor effect. This

machine would not run on its own but, although very dodgy

to ride, it was not as impossible as he had hoped. The

central part of Jones' paper is taken up with deriving a

set of curves for the effect of lean angle on the castor.

This is an alternative method of working out the effective

trail distance which is dealt with in the next chapter

41


using the geometrical method which Jones preferred to

avoid.

Jones had hoped that, by removing the various features

which were supposed to produce stability, he would be able

to identify the contribution each made by finding when the

bicycle became unridable. He confessed himself baffled by

his own ability to overcome the obstacles he devised. The

only modification which makes control impossible is to

lock the steering solid. Since his modifications had the

expected effect on the stability of the bicycles running

without a rider it is evident that humans can deal not

only with bicycles without any stablity but even manage

those which have been quite seriously destabilized.

A more recent study by Lowell & McKell (1981) models

some aspects of bicycle stability. The authors do not

claim this as a serious investigation of bicycle or rider

performance, but rather as a formal application of

classical mechanics to a familiar problem. In order to

keep their equations tractable they ignore both rider

inputs and gyroscopic effects which lead to some rather

strange conclusions about inherent stability which are not

born out by the behaviour of bicycles, and particularly

motor-cycles at high speeds. They quote Jones paper to

support the claim that bicycles with small castor are very

difficult to ride but in doing this they fail to

distinguish between a zero castor and a negative castor.

As will be seen later in this paper reducing the standard

castor of a normal bicycle to zero produces no handling

problems and actually gives the steering a rather pleasant

'light' feel. In any case they are misrepresenting Jones'

report since he did not make a bicycle with zero castor

and even found he could ride URB IV, with its large

negative castor.

42


Lateral Weight Shift as a Control Input

Many studies have considered lateral body shift as a

possible means of control. (Lowell & McKell, 1982; Nagai,

1983; Van Lunteran & Stassen, 1967; Weir & Zellner, 1979).

Although there can be no doubt that bicycle riders do move

their upper body from side to side during riding it does

not follow that this movement is being used to control the

machine either in roll or in direction. However, it is

equally clear that rolling movements of the bicycle frame,

induced by counter movements of the riders' body, will

produce control effects via the autostability effect of

the front fork design. Roll velocity is converted by the

gyroscopic effect into a steering couple away from the

upper body lean. The resulting turn will push the centre

of mass in the direction of the initial lean. A permanent

lean to one-side will also generate a steering torque in

the same direction due to the castor effect. These effects

are confirmed by the fact that riders can control bicycles

with body movements alone when riding hands-off. As far as

this study is concerned, it is important to get this point

quite clear as the integrity of the recordings depend on

the argument that when the autostability of the bicycle is

removed body movements do not produce any significant

control inputs. What must be established is that body

movements in relation to the bicycle frame cannot in

themselves produce controlling forces independent of their

secondary effect via autostability. A preliminary

examination might suggest that an unwanted displacement of

the centre of mass to one side could be removed by leaning

the body in the opposite direction. The dynamics of the

system are, however, principally concerned with the

position of the combined centre of mass in relation to the

road support point and will be affected in a complex

manner during the movement of the rider's mass in relation

43


to that of the bicycle.

(a) (b)

Figure 3.5 Despite the angle between the upper body and the bicycle frame (AL) the centre of mass, shown by the larger segmented circles, does not produce a restoring couple. Drawing (a) shows how even at quite small angles of lean a large AL fails to take the combined centre of mass onto the correcting side of the ground support point. Drawing (b) shows how, as the angle of lean approaches 90 degrees, the apparent sideways movement of the upper body produces very little change in the horizontal plane.

Exactly what happens when a rider moves his upper body

laterally depends on the relationship between the masses

of man and machine, their rate of movement and the angle

of lean.

To deal with the simplest point first let us take the

case of a rider, at some angle of lean, who has already

moved his upper body towards the vertical in an attempt to

restore the disturbance. Figure 3.5, (a) shows that there

will be some fairly small angle of lean where the lateral

44


movement of the body will not put the combined centre of

mass on the restoring side of the vertical from the

support point. In such a case the movement will have

reduced the disturbing couple to the left but will not

provide a restoring couple to the right. Figure 3.5, (b)

shows that at large angles of lean the lateral movement

has a decreasing influence on the disturbing couple as the

movement lies increasingly in the vertical plane.

The above situation is static. How the rider achieves

his displaced position and what happens during the

movement have not been considered. For a start it takes

time to move from the normal riding position to the

position shown in figure 3.5, (a). During the time that

the rider is moving right in relation to the bicycle

everything will be falling left because the combined

centre of mass is displaced to the left of the support

point. This means that the angle of displacement to the

left at which the rider started to make his correcting

move will be less than the angle shown.

Given an initial displacement to one side, whether a

rider can EVER produce a correcting movement in this

manner depends on the interaction between two rates of

movement and the relative moments of inertia of the masses

moved, and this in turn depends on exactly how the rider

carries out the movement.When the rider, seated normally

on the bicycle, is displaced from the vertical so that the

centre of mass is no longer vertically above the point of

support the disturbing couple formed by the weight times

the horizontal distance of displacement produces an

accelerating roll about the support point.As the

displacement increases so does the rate of acceleration.

In order to check this movement two things are necessary.

First either a couple must be formed that will oppose the

accelerating couple or the couple must be removed. Second

an additional couple must be formed temporarily which will

45


decelerate the existing roll velocity to zero at which

point it must then be removed to prevent its starting a

fall in the opposite direction. LI

~Ll

(a) Angular acceleration clockwise:-

(b) Angular acceleration clockwise:-

W * Ll I M * 10 (W * Ll I M * Io)+(F * H I (M-m) *10)

h T H

---,--1 (c) Leg movement

Figure 3.6 showing the acceleration when a limb about a narrow support details. M is total mass,

46

effect on angular is moved to balance

point. See text for 'm' is mass of arm.


In the case which is being considered here the only

means the rider has of providing these couples is to alter

the relative disposition of the physical parts, such as

his limbs or torso, or the bicycle, to somehow move the

centre of mass over to the other side of the support

point. Nothing else will achieve the desired result. The

start position is shown in figure 3.6, (a). The view is

from the rear so that picture left is also left for the

rider.

If it is assumed that in the start position the rider

is sitting on the saddle then the only way he can shift

the centre of mass to the left is by moving some part of

his body in that direction. The argument is easier to

follow initially if we consider the effects of moving

first an arm and then a leg. Figure 3.6, (b) shows the

effect of rapidly pushing the left arm out to the side.

The force needed to accelerate the arm to the left will

act against the shoulders in the opposite direction. The

rate at which the arm moves is given by the force divided

by the mass of the arm (F/m) The rate at which the

remainder of the mass moves the other way is given by the

rotating couple formed by the force times the height of

the point of application above the ground (F*H) divided by

the moment of inertia about the ground contact point

(M*(h A 2)/3). Thus the effect of flinging the arm out leads

to its moving one way and the body moving the other, each

at different rates. While this is taking place the whole

is being rotated to the right under the influence of the

original couple formed by the total weight times the

lateral displacement (W*l) divided by the combined moment

of inertia «M+m) * (h A 2) 13). Thus there are two couples

driving the combined mass to the right but the movement of

the arm out to the left brings the centre of mass out to

the left with it so the lateral distance '1' is being

reduced. Because the arm is by comparison light and is

47


going in a straight line it moves much quicker than the

remainder of the mass. Whether this succeeds in moving

the centre of mass onto the left hand side of the support

point before it rolls out of reach or not depends on the

actual masses and rates involved. To check the roll to the

right the centre of mass must move not just back to the

upright but beyond it in order to remove the accumulated

angular velocity to the right.

An idea of how little control is available using this

method may be gained by standing on one foot on a

laterally unstable platform, such as a rolling pin, and

trying to check an incipient fall by flinging out an arm.

It is immediately evident that the movement of the centre

of mass is not sufficient to overcome the roll. It is just

possible with care to provoke a fall towards the flung out

arm from the in-balance position but there is very little

margin for error. When a leg is moved rather than an arm

the result is more encouraging and there is certainly very

little difficulty in preventing the initial fall from

developing. It can be seen from figure 3.6, (c) that the

thrust which pushes the leg out acts much lower down. The

couple acting to the right now acts over the much reduced

distance H and consequently more of the movement will take

place at the leg. Because the leg is heavier it will have

greater influence in bringing the centre of mass back

towards the centre. Arm and

considered as candidates for

leg movements are not being

bicycle control. The only

other movement available to the seated rider is to bend at

the waist and force the upper body to one side which will

of course force the lower body and the bicycle in the

opposite direction. If the balancing act described above

is now tried using upper body lean to counter incipient

roll by leaning away from the movement the task will be

found to be impossible. In fact a careful attempt to

initiate a fall from the balanced position by a sharp

48


bend in the body will show that there is if anything a

tendency to go the other way, that is the force applied

has a greater effect on the lower mass than the upper.

The masses of the two parts being moved are now more

nearly equal and the thrust is being applied well up the

body. None of these control movements has any chance of

restoring balance once the combined centre of mass has

moved more than a degree or two out of the vertical or

when there is any amount of accumulated angular velocity.

Thus we can see that although a rider can control a

bicycle entirely by moving his upper body away from a fall

this is achieved via the autocontrol effect. Even at very

small angles of lean such a movement cannot alter the

position of the centre of mass to provide a restoring

couple. A clear demonstration of this can be made by

trying to balance on a stationary bicycle using upper body

movements. Providing the chain is disconnected from the

rear wheel to prevent dynamic forces being transferred

through the front wheel this task is impossible and shows

that upper body movement on its own cannot exert control

in the rolling plane.

Indirect Lean Control

Despite the ineffectiveness of lateral body movement as

a direct means of control the automatic stability

conferred on bicycles by virtue of the front fork design

does allow lateral upper body movement to control both

roll and direction. Rolling the upper body to one side can

only be achieved by rolling the machine in the opposite

direction. This roll is converted by the gyroscopic

effect into a steering couple away from the upper body

lean. The resulting turn will push the centre of mass in

the direction of the initial upper body lean. A permanent

lean to one-side will also generate a steering torque in

the same direction due to the castor effect. Since the

49


roll and turn effects achieved in this manner can be

equally achieved by handle-bar movement, and since

the movement of the handle bar is recorded on

only

the

experimental bicycle, it is preferable to avoid the

influence of upper body movements in the analysis. As has

already been mentioned above, it was necessary to remove

the autostability from the experimental bicycle to prevent

a confusion between automatic forces and human forces. By

the same token, in the absence of automatic control, any

body movements made by the subjects will not be translated

into control movements thus forcing the subjects to depend

on hand movements only for control.

The Psychological Point of View

In general the work that has been done on single track

vehicles has been in the engineering field is therefore

orientated towards vehicle design and performance leaving

virtually untouched those aspects of bicycle-riding which

interest the psychologist. Over the past thirty years a

number of engineering theories such as feedback control

and servomechanisms have been adopted by psychologists to

describe the way limbs are controlled during skilled

movements. In 1947 Craik found that people often made

corrections in aiming and tracking tasks in steps rather

than continuously and consequently described this

behaviour as an intermittent servomechanism. Keele &

Posner (1968) estimated that the minimum refractory period

was 260 msecs. Many experiments used tracking or aiming

tasks to explore control which led to a general conclusion

that there is some minimum period required for central

control to detect an error and implement a correction.

When action followed stimulus at less than this interval

it was supposed that control was via a local reflex. This

idea became so well established that the 200-250 msecs

latency was frequently taken as being the criterion for

50


judging whether an action was under central control or

not. However much shorter delays than this have been

recorded in tasks where reflex control seems an inadequate

explanation. For example Cordo and Nashner (1982), whose

experiments will be dealt with in greater detail in

chapter 8, found compensatory postural movements in humans

in the latency range of 70-150 msecs which could not have

been simple reflexes since they adapted to changes in the

environment which could only have been processed

centrally. These discoveries have led to the

classification of responses into three speed categories.

The fastest spinal, or myotatic, reflex acting in the

40-50 msecs range, the centrally controlled decision range

starting at around 200 msecs and between these two there

appears to be a range of reflex like movements, known as

the Functional Stretch Reflex (FSR), which are

nevertheless under some degree of central control.

It would unwise to assume that because intermittent

control is used in some tasks that this is a general

limitation in all tasks. Whether continuous or

intermittent control is used depends initially on the

exact details and in some cases at least it is evident

that the experimental design itself forces a choice of

technique. For example both Pew (1966) and McLeod (1977)

used a tracking task in which the subjects were asked to

keep a cursor in the middle of a VDU screen. The cursor

was always accelerating at a fixed rate in a horizontal

direction and the subjects were given two keys which

selected the direction of this acceleration either left or

right. Even if the subjects had been able to detect the

rate of acceleration they had not the means to apply a

proportional correction. If the acceleration was high

when they switched directions they had to wait for it to

produce a reversal and if they switched when the

acceleration was still very small the result was a rapid

51


reversal and a fast acceleration in the opposite

direction. They were therefore committed to a particular

form of control by the details of the task. In order to

test this point of view the Pew task was rewritten to

allow continuous control of the cursor acceleration with a

joy-stick. It becomes immediately apparent that an

operator can make use of the proportional response and in

its new form the task is comparatively easy. A record of

operator activity shows a continuous change rather than

the previous intermittent control.

For continuous control it is necessary first that some

variable, relevant to the reduction of error, is

detectable by the operator and second that the means of

continuous control is available. Where these two

conditions are satisfied then any delay between detection

and execution appears as a phase shift between the two

continuous movements of the actuating signal and the

manipulated variable. It is also necessary that the

subject adopts an appropriate strategy since such

variables could be detectable but ignored.

It appears from recent work with the mass-spring

theory (Kelso et al. 1980; Bizzi, 1980 & Schmidt, 1980)

that subjects in the sort of movement to a target task

used for ex,ample by Keele (1968), might be setting the

ratio of opposing muscle length/tension to achieve a final

position, in which case a continuous monitoring and

control of intermediate acceleration would not be

necessary.

Bicycle riding was selected as a naturally arising

complete skill which is so constrained that it was very

unlikely to be amenable to intermittent control at the

lowest level. Because the dynamics are non-linear it was

difficult to see how the control could be linear. The main

questions to answered were whether the control was

intermittent or continuous, which actuating signal was

52


being utilized and what form the output to the manipulated

variable took. That continuous proportional responses are

within the scope of human operators was shown in a study

by McRuer and Kredel (1974) in which subjects were given

tracking tasks with varying system dynamics. When the

control device was of the non-linear acceleration form the

subjects responded by making movements which were

proportional to the rate of change of the system error,

whereas for rate control the output was proportional to

the system error itself. Regardless of the system in use

the subjects adjusted the gain so that the input to the

operator and the output from the machine were of equal

amplitude giving a system gain of 1, thus limiting the

input change to a rate which could be easily followed.

A close study of bicycle riding skill stimulates the

interest of the psychologist in a number of ways. What

exactly is the rider doing in terms of mental operations?

How can the behaviour be so flexible as to allow a rider

to move from a touring bicycle to a chopper or lOOOcc

motor-cycle without any apparent need for reshaping the

basic skill? Is everyone doing the same thing, or are

there distinctive versions of the skill?

experienced riders so

what they are doing?

two-wheel bicycles so

bad at describing

How do children

quickly? Why does

Why are even

the details of

learn to ride

convention say

that once learned, bicycle riding is never forgotten and

is this true? If the skill depends on the automatic

stability built into the front forks of all commercially

available two-wheel vehicles why could Jones ride his

grossly destabilized bicycles without having to relearn

his skill? And, central to the controversies surrounding

Schema models, how much memory and computation does such a

skill demand from the rider and to what extent is it

'ballistic' in the Schema sense of the word? The answers

to such questions depend in the first place on finding out

53


exactly what body movements are necessary and sufficient

for normal bicycle control, and it is this question which

this study aims at answering.

Summary

Bicycle riding was chosen as the subject for the study

because it is acquired by many individuals and, being very

constrained by its instability, it allows only a limited

number of possible solutions. The design of bicycles

which has evolved over the years provides a degree of

autostability which varies from very little at slow speed

to considerable at high cruising speed. The high centre

of gravity and small lateral base of the rider/bicycle

combination gives a bad balance between the destabilising

and correcting couples. This severely constrains the way

in which the correcting force provided by the handle-bar

movement must be matched to the rate of roll if stability

is to be achieved. When leg and upper body movements are

ignored the freedom of movement of the rider is also

severely constrained to the single plane of the handlebar.

A record of handle bar movements and roll rate during free

riding represents the input to and output from the human

control system exercising the skill providing that they

can be isolated from the autostable design of the bicycle.

54


4 • THE COMPUTER MODEL

Mathematical Modelling of the Control System

One of the ways of 'understanding' a time-series such

as the rates of roll and bar angle change during bicycle

riding is to construct a mathematical model of the

process, the model in this context being a formula which

predicts the output values from the input. The best

possible fit is obtained when the residual errors between

the predicted values and the actual values sum to zero and

are independently distributed, that is, the error value

at any point in the series carries no information about

the errors at other points, a characteristic known as

'white noise' .

The normal procedure for constructing a mathematical

model of a process is to run it without any control under

the stimulation of either a random, 'white-noise'

generator or some easily modelled function such as sine

wave oscillation. Thus the input is specified as an

experimental variable and a model which predicts the

output describes the nature of the system without control.

This is known as running the system 'open-loop'. Modern

control analysis techniques allow a very complete

specification of many natural systems in this way

including the regimes in which they are stable and

unstable and thus the sort of control systems which would

be successful in achieving stability.

There are a number of difficulties encountered in

attempting to model bicycle riding in this way. The first

is that such models are merely mathematical devices for

'joining' as it were the input values to the output and do

not necessarily mirror the actual processes under

observation. Such a model may be of great use to an

55


engineer who wants to design an efficient control system

but is of less assistance to the psychologist whose aim is

to understand the human contribution in terms of mental

processes and physical movements. In the engineering world

the control system is a constructed machine and therefore

well understood, the focus of interest being on adjusting

its output so that it produces the desired performance. In

the biological world it is the control structure itself

which is being investigated and its interaction with the

rest of the structure is the means of revealing it.

The second difficulty arises out of the nature of

bicycle riding seen as a system. The 'open-loop'

requirement for the bicycle is virtually impossible to

meet because the behaviour of the machine is going to be

quite different depending on whether there is a rider

sitting on it and whether he is holding onto the

handle bars or not. Although the rider's weight could be

simulated a run would still be impossible because without

control the machine will not stay upright. It might be

possible to do very short runs under the influence of say

a short wave sine oscillation accepting a fall at the end

of each run. However the behaviour of the front wheel

assembly, essential to the machine's response, would be

quite different if free to turn than if the rider's arms

were resting passively on the bar. Since human muscle has

a resting 'tonus' or quiescent activity level, and is also

capable of reflex responses to length changes and

pressures it is virtually impossible to specify what a

'no-control' state in the rider might be.

Mathematical models of control systems are equations

showing how the variables behave in relation to each other

over time. The functions are continuous and the

introduction of either discontinuous inputs or changes

that are arbitrary or 'external' to the system invalidate

them. It was strongly suspected from the first that

56


bicycle control was at least partially intermittent and it

was also seen that it would be virtually impossible to

ensure that the rider did not introduce changes during a

run which were independent of the feedback of the

bicycle's movement.

As has already been mentioned in chapter 2 existing

studies of bicycle dynamics have dealt mainly with the

problem of trying to express the stability of the

mechanical system in equation form with a minimum

contribution from the rider. In the interests of

simplicity various aspects not relevant to the particular

study were omitted. For example Van Lunteran and Stassen

(1969) ignored centrifugal forces and assumed a front fork

assembly with zero mass and Lowell and McKell (1982)

ignored both gyroscopic effects and rider inputs.

The Incremental Model

In order to meet these difficulties it was decided to

construct a discrete step model of the mechanical aspects

of the bicycle/rider unit which reproduced as nearly as

possible the responses to handle bar movement in each time

interval. The control sequence which moved the bar would

be modified to test a variety of control solutions,

including intermittent inputs. The output characteristic

would then be compared with that from a real run.

The bicycle/rider combination was broken down into

simple units and each of these was modelled independently

to determine the movement over a single discrete time

interval. The new state of each section at the end of the

interval was then used as the starting point for the

determination of the changes in the next interval. Where

there was a lack of information about performance

empirical values were taken from a real machine for the

range of speeds and angles that were of interest.

The programs for the computer simulation are printed in

57


appendix 1, (a) As is common with programs which have

been developed over a period of time some of the variable

names are somewhat cryptic. In the following text

descriptions of operations will be kept as self-contained

as possible using for the most part abbreviations local to

the paragraph. When names are used which also appear in

the programs they are in single quotes except in the body

of equations where this convention is not followed to save

space on the line. BBC basic uses the % sign after a

symbol name to denote an integer. These are not shown in

the text. The simulation can model either the normal

bicycle or the experimental bicycle, which has all the

autostability removed. A full description of the latter

appears in the next chapter, but it will be referred to

from time to time in this chapter as the 'destabi1ized

bicycle' .

The programs were divided into a number of units

because of limited memory in the graphics mode. There are

several versions of the main program to accommodate

differences in control and output printing. Initial

variables for a run are set up in the program BIKE and

passed to the main program either via the data file VALS

or the BBC universal integer set, A to Z. Data specific

to the bicycle model being run are in the files BIKE_A,

BIKE B etc. These files also contain the moments of

inertia which are calculated separately in the programs

BIKEIN and MOMENTS. The details of any bike can be printed

with the routine CBIKE. The routine SCALES draws the axes

for the main program.

The input to the main program consists of changes to

the force applied to the handle bar. These are either

fully automatic or can be introduced from the keyboard.

The output takes the form of a five axis graph with

selected values, such as roll angle, velocity or

acceleration plotted vertically against time. The program

58


can be stopped as required and the screen contents

printed. Many examples of the output appear in this and in

the following three chapters. It should be noted that the

names for the variables printed in these figures are

different from the names used in the computer program. The

convention followed is to use a single quote mark to

denote the first derivative of the angle, ie velocity, and

two for the second, ie acceleration. Thus, for example,

roll velocity is written as R' and steering acceleration

as SI I.

The rider/bicycle system is considered to consist of

two parts, the frame and rider as one unit and the front

wheel, forks and handle bar as the other. Within the

latter part the rotation of the front wheel was also

modelled for the precessional effects on

difference in moment of inertia of the

steering. The

frame between

having the steering straight ahead and at some large angle

is small so it is ignored. Throughout the text the

convention applies where rotation about the fore and aft

axis is called roll and that about the vertical plane,

yaw. The speed was a constant which could be altered at

the start of ~hy run. No account was taken of linear

accelerations or retardation forces.

The difficulty in modelling the movements of the

bicycle in three dimensions is finding tractable

equations. One way to circumvent this problem is to model

some limited p~rt of the action only. If, however, all

the main ingredients are to be represented then something

else has to go. In this model that something is the

strictly accurate relationship between the various

contributing forces. In the rolling plane this is not

very critical as small accumulating errors only give a

change in degree. That is,

from the steerihg angle will

in correcting for unwanted

59

insufficient contribution

lead to a 'sloppier' response

roll angle. When the two


couples balance to produce zero roll velocity then the

system will be re-zeroed. In the yawing plane however the

relationship between the planes of rotation of the two

wheels and their local relative movement over the ground

is very critical as errors here can lead to a reversal of

sign which plays havoc with the turning performance.

Hence it will be seen that much greater attention has been

given to the yawing forces in the main program. The same

applies to the calculation of the effective trail distance

with changes in roll and steering angle as this is

critical for the autostable forces.

mgrav4 Mhtj mgrav3 bgrav4 S

i " IvmgraV2 I:::::;:s;I

comb.lgth

mgrav 1 ,r-1i"=~L!!..!~t&bgttav2 rake Mrad

effe!tive height bgrav 1

! ! wheel base

. • t rl (

effective length )

Figure 4.1 Showing the location of the values stored in the bicycle data files.

Rider and Bicycle Dimensions

The Triumph 20 bicycle used for the experimental runs

was dismantled, the parts measured and weighed using a

steel rule and a spring balance. The rider was regarded as

a regular vertical cylinder with no allowances made for

limb movements. The weight used for the illustrations in

60


this thesis, at 11.5 stones was the mean weight of the two

subjects involved in the experiments. The centre of mass

of this cylinder was positioned 6 inches above the saddle.

The coordinates for the positions of the centres of mass

were taken from a scale drawing of the bicycle which is

reproduced in appendix 1, (b). For the calculation of the

moments of inertia the bicycle was considered to be a flat

plate with no lateral dimension. Since the wheels are

considerably lighter than the rest of the frame the

effective length and height of this plate were taken from

the 0.6 radius point of the wheels. The figure 0.6 was

taken as a compromise between the radii of gyration of a

solid disc and a wheel with all the weight at the rim, ie

0.5 and 0.7 respectively. All the above values were fed

into the file BIKE C using the routine BIKEIN.

Moments of Inertia

The rbutine MOMENTS uses the data for the specific

bicycle to calculate the moments of inertia used in the

main program and store them with the other dimensions in

the BIKE_A type files. Figure 4.1 shows the dimensions

used in this routine and table 4.1 shows the values for

the Triumph 20 bicyCle used in the experimental runs.

Where the same names are used in the following text they

appear in single quotes, except in the equations.

61

Bicycle Riding

Measurement

Wheel base Front wheel radius Rear wheel radius Effective height of bike Effective length of bike Rake angle Trail (trl) Bike mass Front wheel mass Bgravl Bgrav2 Bgrav3 Bgrav4 Man ht. Man rad. Man mass Mgrav1 Mgrav2 Mgrav3 Mgrav4 Combined mass Combined weight Combin~d C of G height Combined C of G length Bar effective length Bar mass

Moments of Inertla

Vertical about road. Vertical about C of G. Horizontal about C of G.

Program name

WB Wradl

rake trl

Mass WT RG

bar

WIO FIo RIo

Horizontal about rear wheel LIo Front wheel assembly FwIo

Value

3.28 0.85 0.85 2.79 4.26 20.0 0.15 1.0 0.1 1.39 1. 89 1.39 0.13 6.0 0.75 5.00 3.64 0.36 1.23 0.00 6.00 192.0 3.28 1.27 1. 70 0.10

84.53 20.57 2.935 12.42 0.060

Chapter 4

Units

ft ft ft ft ft degs ft slugs slugs ft ft ft ft ft ft slugs ft ft ft ft slugs lbs ft ft ft slugs

Table 4.1 The dimensions for the Triumph 20 bicycle used in the runs. These data are stored in the file BIKE_C. The moments of inertia are generated by the program MOMENTS.

62


The moments of inertia about the centres of mass for

the cylinder representing the man and the plate

representing the bicycle are worked out first as follows:-

vertical Moments

man mom = man mass * ('Mrad'A2)/4 +

bike mom = bike mass * (bike ht A2)/12

Horizontal Moments

man mom = man mass * ('Mrad'A2)/2

('Mht' A2) /12

bike mom = bike mass * (bike lengthA2)/12

steering Moments

bar mom = bar mass * (bar lengthA2)/12

Fwheel mom = Fwhee1 mass * ((wheel rad * DE)A2)/4

where DE is the conversion for a wheel with its mass at

the rim to an equivalent uniform disc. (=1.4144)

The combined moments of inertia are now worked out

using the parallel axis theory. The general equation is:-

Combined mom = mom about C of Mass + (mass * (PD A2»

where PD is the separation between the axis under

consideration and a parallel axis through the centre of

mass. The various combined moments are listed with their

program names and the relevant values of PD:-

Vert. about road 'WIo' ............. 'Mgrav1 " 'Bgrav1'

Vert.about C of M 'FIo' ............. 'Mgrav2', 'Bgrav2'

Horz. about C of M 'HIo' ............. ' Mgrav3 " 'Bgrav3 '

Steering moment 'FwIo' ...... .... bar mom + Fwheel mom

63


Side Force at the Wheel/Ground Contact Point

Whenever an object runs in a curve a force at right

angles to the direction of travel must be present. This

force comes from the action of the wheels running at a

slight angle to their direction of travel, dragging the

tyre over the ground. The theory governing the forces

produced at the tyre/road contact point is too complex and

incomplete to allow its use in this part of the model.

However it is evident that the general characteristic of

more angle more force holds good up to some critical angle

where the tyre stalls and the force becomes very large and

is directed almost entirely backwards as drag opposing

forward movement. It is also obvious that the force for a

given angle is dependent on the speed. It was therefore

possible to run a bicycle in a turn and, knowing the

weight of the system, the radius of turn and the speed,

calculate what the force towards the centre must be. This

method was not very precise, but all that was required was

some guidance of the size of force per wheel to ground

angle and an idea bf whether it varied directly as the

speed and angle or in some more complex relationship. Once

an approximate value was obtained it could be trimmed in

the simulation to suit a range of useful speeds.

When a bicycle runs in a steady turn the radius for the

front wheel is greater than that for the rear. This

difference in turning radius was found by measuring the

wheel tracks, allowing a reasonably accurate estimate of

the angle at which the rear wheel was dragging to produce

its contribution to the turning force. When the system is

in a steady turn the force at the front wheel must be

slightly in excess of that at the rear to maintain the

rotation but this difference was ignored in establishing

the force per wheel, that is the total force was divided

equally between the two wheels.

64


The following measurements were made with a 170 lb

rider on the Triumph bicycle (weight 30 lbs). The speeds

were estimated approximately by timing the pedalling rate

for a distance of 70 yards prior to entering the turn. The

steering angles were estimated by eye against a marked

scale fixed to the frame and are very approximate. These

are not used in calculating the estimated flow angle for

the rear wheels but served to confirm the fact that

both wheels were dragging over the ground at

approximately the same local angle. The runs were made on

a newly swept sand surface and left very clear marks from

which the radii of the turns were measured with a steel

tape. Each turn was made through 360 degrees.

Speed Steer- Radius Rad.diffs Drag- Force per

angle angle wheel

(ft/sec) (degs) (ft) (ins) (degs) (lbs)

15 5-10 26 2-3 0.5 27

10 10-15 18 3-4 1 17

10 15-20 11 4-5 2 28

The last run was almost at the adhesion limit for the

tyres on the loose surface and when the turn was tightened

the radius difference increased to about 5.5" and then the

wheels slipped. The drag angles were measured from a large

scale drawing of the radii and bicycle frame and are

approximate. Because of tyre distortion under load the

relationship of force to both angle and speed is not a

simple straight line. To obtain an approximate

relationship for these two factors it is assumed that the

force increases directly with angle. If the first and last

runs are then considered it can be seen that they generate

much the same force since the larger radius turn is

performed at a higher speed. If the same angle

relationship is applied it will be seen that the speed

65


factor must mUltiply the force effect by about 4. This is

very approximately equivalent to a cube function of speed.

Raising the speed to the power 2.7 gives a fairly

consistent coefficient of .03 for the three runs but is of

course very rough. However this was sufficient to guide a

choice of values for the simulation which after some

trimming was taken as speed raised to the power 1.8 with a

coefficient of 0.2.

Force drag angle(degs) * (VVA1.8) * CD

where 'VV' is the speed and 'CD' is the drag

coefficient. This keeps the system stable within the speed

range 2 to 15 mph which is all that was required.

The side-force is frictional and will therefore depend

on weight. Because the tyre is not rigid it will distort

with different loads so the exact relationship between

weight and force is not known. In order to allow for this

change the coefficient is made directly proportional to

the weight. This is established in the line:-

CD 0.0014 * WT

which must of course come before the line given above.

This gives a satisfactory performance over the weight

range 32 lbs (riderless bike) and 284 lbs (18 stone

rider) .

In reality it is obvious that there is much more to

tyre

that

behaviour than is captured here but the main point is

despite very large differences in tyre type and

riding condition all bicycles behave in approximately the

same way so exact details within those limits which allow

a stable performance are not important for the model and

did not justify a more exact measurement on the real

bicycle.

66

Bicycle Riding

Rotations

The linear

in the Horizontal Plane

speed of the machine is

Chapter 4

assumed to be

constant and no account is taken of fore and aft

retardation forces. The mass of the bicycle/rider unit

will not travel in a curve unless there is an unbalanced

force acting at right-angles to the local direction of

travel. This force must be generated by the wheels

'dragging' at an angle to their local direction of travel.

Once in a turn the relative movement between the ground

and any point on the bicycle is represented by the tangent

to the turning circle at that point. With any turning

system whether it is a car, a bicycle, a boat or a ski,

this relative angle will only be the same for all points

when they lie on a common radius. Thus ,since all such

systems are orientated normal to the radius and more or

less facing the direction of movement it follows that

there will be a difference between the local surface

movement at the front of the object and that at the back.

The controlling ratio is that of the length of the object

compared with the radius of the turn, so for a given

length the tighter the turn the greater the effect. This

difference of surface to object velocity during turning

manoeuvres is critical to the ability of all systems which

use relative surface movement to generate the turning

force, to sustain a controllable turn. Unless some angle

difference is introduced between the front and rear of the

system the increasing curvature of the flow as the turn

develops will produce an out of the turn rotating couple

which will back- off the generating angle and stop the

turn. In every controlled turn the couple rotating the

object must be exactly matched with the total force

controlling the radius of turn in such a way as to

preserve the wheel to ground angles and the forces they

67


generate. It is the lack of tractable equations to

represent this situation which has led to such limited

models of bicycle performance.

Because this simulation uses a discrete step rather

than a continuous solution it is able to establish these

important angles geometrically. The principal reference is

taken as the north axis in the conventional cartographic

sense. Angles are measured as positive from north in the

westerly direction and negative in the easterly. There is

no anomaly in the southern segment as the model does not

exceed 90 degrees either side of north.

At the start of any time interval, 'Ti', each wheel

will have made some angle to the local relative ground

movement in the previous interval. Whenever this angle is

greater than zero a force at right angles to the plane of

the wheel will have been generated, the value depending on

the actual angle and the speed. During the new time

increment the combination of these two forces is regarded

as an impulse acting on the centre of mass which will then

move during the interval under both this influence and the

linear velocity which is defined as a constant. Any

difference in size or direction of the two wheel

side-forces will also cause a rotation during the

interval. The combination of the linear and rotational

movements will lead to different relative paths for the

front and rear wheel contact points which must be used to

find the new forces generated at each wheel during the new

interval. The front wheel is free to rotate in relation

to the frame so this relative movement will also produce a

couple in the steering when the ground contact point lies

anywhere but directly on the extended hinge axis. In the

normal 'autostable' bicycle this is the effective trail

distance.

its own

steering

The front wheel, having

inertia and angular

mass, will also have

velocity about the

axis which will influence the angle it makes

68


with the external reference and the frame. The

precessional effect of the front wheel due to rolling

movements of the frame must also be added to this couple.

Values required in the horizontal plane

'Ti' One increment of time (10 msecs)

'VV' The linear velocity of the centre of mass.

Mass WT Mass and weight of bicycle plus rider.

'RA' Angle between local direction of travel of the

centre of mass and north.

'HA' Angle between the frame of the bicycle and north.

'SA' Angle between the front wheel plane and north.

'RSA' Angle between the front wheel plane and the

frame. (RSA is written as R in the printout figures)

'L2' Angle between the frame and the local direction

of travel at the rear wheel contact point.

'Ll' Angle between the front wheel plane and the

local direction of travel at the front wheel contact

point.

'Hw' The angular velocity of the frame.

'Sw' The angular velocity of the front wheel, forks &

bar. (Sw is written as S' in the figures)

'Roti' Angle of ground 'flow' to frame due to rotation.

'Si' Distance increment travelled by C of M in time

Ti.

'RAi,HAi,SAi' angle increments in time interval Ti.

'HwDOT,Sdot' angular accelerations of frame and front

wheel. (Sdot is written as S" in the figures)

'Fl,F2 & FF' The forces at the front and rear wheel

and their additioh.

'Trl' The effective trail distance.

The method of working out the movement of the ground

relative to the front and rear wheel contact points

(called the ground 'flow') is as follows:-

69


(i) 'FI, F2 and FF' are found using 'LI and L2' from

the previous increment:-

FI= (LI * Ffac) F2=(L2 * Ffac) FF= FI + F2

where 'Ffac' is the frictional coefficient for the tyre

adjusted for speed and weight.

(ii) 'FF' is normal to the direction of travel by

definition. This disregards the difference between the

frame angle and direction of travel but is sufficiently

accurate for the shallow turns under consideration. The

error is a function of radius of turn and rear wheel

ground Ilow angle. For a 26 ft radius turn with 1.5

degrees flow angle it is just over I degree. 'FF' is

applied as an impulse over the time increment 'Ti' at

right angles to the direction 'SA', giving an angle

increment 'RAi':-

RAi ATN(FF * Ti) / (Mass * VV)

(iii) The linear advance in one time increment:

Si = VV * Ti

(iv) Any difference between the wheel forces 'FI' and

'F2' will form a couple rotating the frame. The

increment of rotation ('HAi') is found by combining this

couple with the angular velocity ('Hw') from the previous

time increment:-

HwDOT =(FI-F2) *WBI/(HIo*COS(VA) +(FIo*SIN(VA)

HAi = (Hw * Ti) + (HwDOT * (Ti A 2)*O.5

where 'HIo' and 'FIo' are the angular moments of

70


inertia in the vertical and horizontal planes. 'VA' is the

lean angle and 'WBl' is half the wheel base. Both moments

of inertia have to be considered when there is an angle of

lean. The couple arm 'WBl' is not exact as it will vary

for different systems. For the Triumph 20 it is 0.43 of

the wheelbase, for the Carlton it is 0.5. Now the new

angular velocity may be found:-

Hw = Hw(previous) + (HwDOT * Ti)

(v) In a similar manner the change in the steering

angle ('SAi') is established. The couples acting in the

steering plane are the weight and 'Fl' force acting

through the trail distance of the castor effect, the

steering force acting over the handle bar length and the

precessional effect due to any roll angular velocity

present:-

Sdot = (PC*Vw)+(SF*bar)+(Fl*Trl)+(WTl*SIN(VA)*Trl)/FwIo

SAi = (Sw * Ti) + (Sdot * (Ti A 2) * 0.5)

where 'PC' is the precessional coefficient, 'SF' is the

steering force, and 'FwIo' is the front wheel angular

moment of inertia about the steering axis. Strictly

speaking WTl should be the proportion of the weight

falling on the front end of the machine. In practice this

is taken as being equally divided fore and aft, so WTl is

(WT/2). The force due to the precession of the front wheel

is:-

Moment of Inertia * angular velocity of wheel

* roll velocity

The first two terms together are the angular

momentum, 'PC', which is established with the line:-

71


PC (Fwlo*2) * (VV * pi * 2 /(front wheel diam * Pi»

The moment of inertia is multiplied by 2 because the

stored value is the inertia about the steering axis which

is half that about the axis of rotation. The expression is

only solved once for any run so, in the interests of

readability in the program it has not been simplified any

further.

The new angular velocity of front wheel unit is:

Sw = Sw(previous) + (Sdot * Ti)

HCi ........... front wheel

frame

~" / Rot i frame at start / ofTf

HAi

HCi

Roti

reference north

Rear wheel

Figure 4.2 Finding the local ground/wheel 'flow' angles during a turn.

Finding the Front and Rear Ground Flow Angles

Figure 4.2 shows the translation and rotation of the

frame during a time interval 'Ti'. During 'Ti' the frame

advances in the direction 'RA' from A to B, a distance

'Si'. without rotation it would end up

shown by the dotted lines with the

72

in the position

front and rear


extremities having traced out paths with the same angles

to the direction of travel. In the situation envisaged it

is supposed that an imbalance between 'Fl' and 'F2'

rotates the frame to the left through the angle 'HAi' and

the front and rear of the frame move through the distance

marked as HCi. The ground flow at the front of the frame

alters by the angle 'Roti' so that it comes more from the

left, that is the flow angle is increased while that at

the rear is decreased by the same amount. The angles 'RA'

& 'HA' have been exaggerated in the diagram for clarity,

but for the small angles of flow normally encountered HCi

may be regarded as the common arc of the two triangles

giving the relationships:-

HCi = HAi(Rads) * half the frame length

Roti(Rads) = HCi/Si

The relationship of the ground flow at the two ends of

the frame to the external reference is:-

Front RA + Roti Rear RA - Roti

Signs of the Angles

Strict attention must be paid to the signs of the

various angles to ensure that their correct relationship

is preserved for all conditions. These are:-

'RA' positive to the left, negative to the right

'HA' positive to the left, negative to the right

'Hw' positive when rotating anti-clockwise

'Roti' takes on the sign of HCi which in turn takes the

sign of 'Hw' via 'HAi'. The other conventions adopted

are:-

73


Flow Angles. positive

front of the frame

when that flow applied to the

would lead to a positive

(anti-clockwise) rotation.

Forces ('Fl,F2') positive when causing an

anti-clockwise turn.

The resulting rule for maintaining the correct

relationship at the rear wheel under all conditions is:-

L2 HA - (RA - Roti)

Since the front wheel is free to steer under the

influence of the road and bar forces its angle ('SA') must

be measured in absolute terms. Once its resulting position

for a time increment has been established then the

relative angle ('Ll') it makes with the ground flow can be

found. The sign convention here is:-

Front wheel to frame ( 'RSA' ) positive when

anti-clockwise.

Front wheel flow angle ('Ll') positive when causing an

anti-clockwise rotation.

The rule for finding 'Ll' is:-

Ll SA - (RA + Roti)

and the relative steering angle is:-

RSA SA - HA

74


Order of calculating the variables

It is obvious that the exact place in the routine where

values are updated will make a difference to the outcome

and so their sequence must be chosen with care.

Variables common to several equations, such as velocity,

must be updated at the end of the period. It will be seen

in the programs AUTO and DESTAB in appendix 1, (a) lines

6000,6999 that the sequence is:-

Forces (F1,F2,FF) from previous angles (L1,L2)

Accelerations New forces, old velocities, trail & bar

force

Angle increments. New forces & accelerations, old

velocity

New flow angles Roti,L1 & L2

New velocities

New trail distance and bar force.

Rotation in the vertical Plane

Roll is influenced by two couples. First the weight

acting over the horizontal distance from the support point

of the wheels when there is an angle of lean, and second

the side fo~ce acting through the tyre contact points

acting over the vertical distance from the ground to the

centre of mass. This latter couple is exactly the same as

the centrifugal force acting over the same distance. The

way the moments of intertia interact with these two

couples

rotates

in altering the

the rider /bike

roll is complicated. The weight

combination about the ground

contact point but when the bicycle is turned to counter a

fall the action of the wheels on the ground does not pull

the centre of mass back up to a position above the contact

points but moves them in under the weight as it were. The

75


equations which express this relationship do not resolve

into convenient values. For the program however the

general situation can be simply expressed in this way.

More lean means more acceleration into the fall and more

ground/wheel angle means more acceleration out of it. The

values for these couples are easy to find so the problem

rests in finding suitable values for the inertias or

viscosities of the response to them. As a simplification

of the true situation the moment of inertia used for the

weight acceleration, 'Wlo', was taken about the ground

contact point and that for the tyre-force, 'Flo', was

taken about the centre of mass. In practice this solution

works well and there was no need to trim the values.

The values used for working out the roll rate are:-

'VwDOT'

'Vw'

'VA'

'WIo'

'Flo'

'HG'

'FF I

Angular acceleration in roll (R" in figs)

Angular velocity in roll (R' in figs)

Roll angle (R in figs)

Moment of inertia about ground contact point

Moment of inertia about centre of mass

Frame height of CG above ground.

Combined side force from tyre/ground points.

The acceleration in roll is found with the line:-

VwDOT=((WT * SIN (VA) * HG) / Wlo)

+ ((FF * COS (ABS (VA)) * HG * -1) / Flo)

'FF' is the value found in the previously described

horizontal rotation section. Note the correcting couple

takes the reversed sign of this value not the lean angle.

The increment, angle and roll velocity for Ti are found

in the same way as the equivalent values in yaw:-

76

Bicycle Riding

VAi = (Vw * Ti) + (VwDOT * 0.5 * Ti A 2)

VA = VA(previous) + VAi

Vw = Vw(previous val) + (VwDOT * Ti)

Chapter 4

and the order of calculation must be adhered to.

Calculating the Effective Trail Distance

The effective trail distance is the distance from the

ground/tyre contact point of the front wheel to the

steering axis measured perpendicular to the axis, (see

figure 4.3). As the steering angle increases so this

distance reduces. For any steering angle the distance also

reduces as the angle of lean increases.

RAKE

TRAIL J " I , --1l15li/

Figure 4.3 Showing the effective trail distance in relation to the front wheel and front forks.

At varying combinations of roll and steering angle the

distance reduces to zero and then increases in the

opposite direction. At small lean and steering angles

when the distance is positive it provides part of the

autostability of the bicycle and is therefore a vital

ingredient of the model. There are three ways of

finding this distance. (1) Make selected phys ical

77


measurements on a real bicycle at different steering and

lean angles. (2) Describe the front fork and frame in

space coordinates and apply the appropriate

transformations. (3) Apply spherical trigonometry. Of

these three the last is the only one which will provide an

accurate value for all combinations of angles without

taking up either too much memory or too much computation

time. The equations are complicated and would take up a

great deal of space to explain in detail, thus the final

solution only is given. The other two methods were used

to provide a table of selected values as a check on the

accuracy of the method used.

Variables External to the Subroutine

'RSA' Angle between the front wheel and the frame

'VA' Angle between the frame and the vertical

'RP' The front wheel radius

'HL' The rearward 'rake' of the steering axis

'R90' Rad of ninety degrees

'Ld' Zero angle trail distance

First the signs of the steering and roll angle are

adjusted:-

SA ABS (RSA) VA = ABS(VA) * SGN(VA) * SGN(RSA)

SD = (ATN(TAN(SA)*SIN(HL))

Some abbreviations to simplify the layout:-

CD = COS (SD) CH = COS (HL) SW = ACS(CD * CH)

78


Then:-

b RP * COS {ACS [(CH-(CD*COS(SW»)

/ (SIN (SD) * SIN (SW) ) J) theta = (R90 + (VA + SD»

GA = ATN {b / (RP * -1 * TAN (theta»)

trail = {(RP * SIN (GA - SW» + Ld)

The Printed Graphs of the Simulation

With the exception of two graphs which show the output

in the horizontal for direct comparison with the actual

recordings, all the figures showing the performance of the

computer simulation take the same form. With reference to

figure 4.4, which is the first of these diagrams, it will

be seen that a brief title identifies the model and the

speed at which it is running. The output is displayed on

five vertical axes with zero time at the bottom. Seconds

are displayed in the left margin. At the top of each axis

is a bar and above this a figure in brackets which shows

the value along the X axis of half the bar. Above this is

a letter which identifies the variable running on that

axis. These are the same for all the diagrams and read,

from left to right:-

R Angle of lean (roll) in degrees

S Steering angle relative to bike frame in degrees

R" Roll angular acceleration in degrees/sec/sec

S" Steering angular acceleration in degrees/sec/sec

R' Roll angular velocity in degrees/sec

Testing the Model

With the discrete time increment method employed in

the model the changes are never absolutely accurate as

there is no feed-back between functions during the

interval. For example changes to the steering angle during

79


time Ti would obviously affect the rate of frame rotation

so that the predicted change in frame angle due to the

previous wheel angles will never be quite correct.

Secs

J.

Secs

BIKE....E R

( 2)

BIKE....E R

( 2)

5 mpb S

Riderless (Destab)

( 7)

'- ]"'--'--

5 mpb S

( 7)

R·· S·· (10) (10)

Riderless (Normal) R" S"

(10) (10)

R' (5)

R' (5)

Figure 4.4 The behaviour of the simulated Triumph bicycle without a rider pushed off at a speed of 5 mph. Speed decay is not simulated. The top graph shows the destablized machine and the lower graph the normal bicycle. See text for details.

It is evident that greater accuracy could be obtained

by operating some recursive procedure which ran through

80


each set of calculations a number of times trimming the

input variables on each run to get the best possible fit

between the competing contributions. However it was

decided to do without this if possible by using very small

time increments and putting up with the long computing

time. The nearer the time increments come to zero the

nearer the procedure approaches a truly continuous

relationship.

As will be seen in later chapters the model reproduces

all the general characteristics of the real bicycle. If

the bar is turned during upright running the bicycle rolls

strongly out of the turn and if then left to its own

devices the autocontrol will restore upright running.

Increase in speed increases the autostable response.

Trimming the tyre response coefficient will adjust the

amount of front wheel movement required to produce a given

lean/turn movement without altering the overall

relationship. The physical dimensions of both the rider

and the bicycle can be altered without changing the

general performance. It is even possible to put some

rather extreme bicycles into the model, such as a penny

farthing or a circus 'tower' bicycle (in which the rider

sits on the top of a six-foot tower with remote steering)

without disturbing the behaviour.

An exact correspondence between the model and the

particular bicycle chosen was not important as the

requirement was to represent the general rider/machine

situation. Any competent rider can ride any normal bicycle

without practice, and it was assumed for the purposes of

the initial model that all riders on any bicycle behave in

roughly the same way. To serve its purpose the model had

only to capture the characteristic behaviour within this

general bracket. When the time interval is too large the

system starts to overcontrol and eventually reaches a

stage of diverging osci llation. A time interval of 10

81


msecs was established as the best compromise. At 20 msecs

there was some sign of instability on hard manoeuvres

and at 5 msecs, any difference was too small to show on

the screen printouts.

Two specific tests illustrate the above

Anticipating the findings of chapters 5 and 6,

points.

a delayed

control system is a more demanding test of the simulation

than the instant autocontrol of the normal bicycle. In the

first test such a system, set at a delay of 120 msecs

and the normal time interval of 10 msecs, will contain an

initial disturbance of 5 degrees of lean within 10.5

degrees of roll. If the interval is changed to 5 msecs the

performance is indistinguishable from that at 10 msecs. If

the interval is increased by a factor of four to 40 msecs

the fall is still checked at 10.5 degrees but the system

is thrown into an unstable oscillation.

The second test simulates pushing the bicycle off at a

smart trot without a rider. A normal bicycle treated in

this way will fall, slowly at first, into a turn one way

or the other. After about 4 seconds the angle becomes

extreme and the bicycle falls rapidly to the ground. The

destabilized bicycle pushed in this way falls to the

ground in about 1 second in the direction of the first

angle displacement.

The real bicycle will slow down during

whereas the simulation has no capacity for

so is slightly slower to fall. Figure

this manoeuvre

variable speed

4.4 shows the

computer printout for the two conditions described using a

launch speed of 5 mph and an initial displacement of 0.1

degrees to the left. In the first there is no autocontrol

and the bicycle falls over in about 1 sec. In the second,

with the autocontrol working, the gyroscopic and castor

effects limit the rate of fall but cannot contain it and

the bicycle eventually falls over in about 4 seconds. The

time to fall for the real bicycle when launched at a fast

82


trot was about 3.5 secs. The failure of the autocontrol

to prevent the fall is mainly a function of the speed. It

will be demonstrated in chapter 7 that when the speed is

high enough the auto stability will maintain straight

running with a rider. If the simulated bicycle is

launched without a rider at 20 mph it runs true and will

recover from disturbing pushes to the handle bar. No test

of the real bike was made at this speed al though the

author heard a first-hand account from an owner who, as a

result of a bet, pushed his riderless bicycle down a steep

hill and it ran upright to the bottom.

It might be thought that changes in weight would have a

large effect on the performance but this is not so.

Because the coefficient of tyre response depends on weight

the increase in disturbing couple is matched by an

increase in tyre effectiveness which keeps the performance

more or less the same. A test of the model with different

riders gave the following responses to a fairly strong

initial disturbance of 5 degrees using the destabilized

bicycle which is a more severe test of the system:-

Wt of Rider Init. disp. Fall contained

(stones) (degs) (by. degs)

5 5 8

11. 5 5 8.9

18 5 7.6

In each case the general characteristic was exactly the

same, that is the bicycle recovered to stable running

after two or three damping oscillations though there

were of course small differences in the detail of how much

bar was used to control the movement. The exact

performance depends on how the coefficient actually alters

with weight, but for the purposes of the study the

performance resulting from the approximation was quite

83


adequate.

Summary

This chapter has introduced the simulation which is

used to test various control sequences. It has avoided the

classical difficulty caused by the lack of tractable

equations by using a discrete step technique which,

although slow in operation, represents the mechanism of

free riding sufficiently accurately to predict performance

of a variety of possible control sequences. In the next

three chapters a close study is made of roll and handle

bar angles recorded during free riding. Control sequences

suggested by this work are tested on the simulation to

find their stability and whether they produce an output

characteristic which matches that of the real machine and

rider.

84


5. THE CALIBRATED BICYCLE

Introduction

The main requirement was to obtain a detailed record of

the activity in the roll plane and at the steering head on

a common time base during

had been

normal free riding.

Before any recordings made it was not known

exactly which information would be of the most value so

provision was made for recording both roll and yaw rates.

It became evident that the yaw information was not needed

and since the number of recording points

any single channel depended on the

per unit time for

total number of

channels in use only the roll and handle bar channels were

used for the main runs.

Angle Change Sensors - Roll and Yaw

Either an accelerometer or a roll-rate meter will

provide the information required but the latter type of

sensor was chosen as it was cheaper and more robust. Two

Smiths Industries type 902 RGS/l Rate Gyros, were mounted

at ninety degrees to each other, one in the vertical

rolling plane and the other in the horizontal yawing

plane. No matter what the angle of lean, the roll sensor

continues to give the correct rate of change but the yaw

meter output is corrupted by any lean,

that depends on the cosine of the

giving

angle.

a response

This was

considered acceptable since the main interest was in the

roll channel and for normal riding the angles of lean were

not expected to exceed ten degrees which means the yaw

output would be within 98% of its true value. The

roll-rate meters are 'tied gyros'. A gyroscope is set in

gimbals which allow movement in the measuring plane only.

Any displacement of the gimbal from zero is detected by

85


an optical sensor which then drives it back to the zero

position via a precessing current applied to a coil

winding. The current is proportional to the rate of

angular movement and this is the detected signal. The

maximum rate is 50 degrees per second which is more than

adequate for the task and the sensitivity is 60

mVolts/degree/sec. The gyros are powered by a 6 volt

accumulator carried on the bike in the instrument box.

Angle Sensor- The Handle Bar

The angle of the handle bar is read from the output of

a sensitive potentiometer geared via a rubber belt drive

to give 360 degrees of potentiometer movement for 106

degrees of bar movemeht. The potentiometer output varies

from +2.5 vdlts to -2.5 volts giving a sensitivity of

.0139 volts per degree of movement. The Zero position of

the bar and potentiometer drive were etched with two marks

that were aligned when the wheel was dead ahead. Some

difficulties were experienced at first with zero drift due

to the '0' ring drive band losing its elasticity. This was

overcome by fitting a thicker band. Zeros were measured

with a special routine during testing but since the main

interest focus sed on the rate of angle change, that is the

differential of the output, exact zeroing was not very

critical.

Speed Sensor

A perforated disc

light-sensitive cell

perforations passed

proportional to the

driven by a road wheel with a

counting the rate at which the

it, produced a voltage output

road speed. Since this device

required its own transmitting channel it was not used in

the main runs in order to improve the density of recording

points for the roll and handle bar channels. Speed was not

a critical factor and was calculated approximately from

86


the length of the run and the time taken.

Transmitting the Output Voltages

Initially a radio relay link was built to transmit the

output voltages from the sensors to the microcomputer for

recording but the problems of interference between the

gyroscopes and the transmitter were never satisfactorily

overcome so a simple cable was used instead. A 5mm

diameter multicore screened cable carried the four output

voltages from the detector box on the bicycle to the

micro-computer. Losses due to cable length were found to

be negligible and the rider was unaware of the slight drag

at the rear of the machine. An 80 ft cable gave about 25

seconds of recording time for a rider travelling very

slowly in a straight line. Longer recordings were of

course possible when turning. Most of the runs were in a

more or less straight-line but no difficulties were

experienced even when several turns were made back over

the cable.

Recording the Output Voltages.

The positive and negative outputs from the gyroscopes

and steering potentiometer were converted on board the

bike to the 0-1.8 volts necessary for the Analogue to

Digital Converter (ADC) in the BBC microcomputer. The

electronics, the gyroscopes and the accumulator battery

were housed in a box that was bolted to the rear carrier

of the bicycle. The transmission wire trailed from the

rear of the box clear of the back wheel. The corrected

voltages were fed directly into the ADC port of the BBC

which was housed in a mobile laboratory with a mains

electricity supply. An assembly code routine running on

the micro read the output from the ADC channels at their

fastest conversion rate which is approximately 10

milliseconds per channel and put the raw data into a

87

Bicycle Riding

reserved memory block. The

brought the time for recording

Chapter 5

additional manipulations

one point to approximately

13 msecs plus a constant 4 msecs overhead regardless of

the number of channels in use. At the end of the run this

block was down-loaded onto disc, clearing the space for

the next run. A short binary file was also stored for

each run giving the run details associated with the raw

data file. Another program measured and recorded the zero

voltage output of the four channels as a check between

runs.

CONTROL OF THE DESTABILIZED BICYCLE

The Experimental Bicycle

A Triumph 20 inch wheel model was used for the runs.

This gave a large range of seat and handle bar adjustment,

allowing any size of subject from large adult to ten years

old child to ride with comfort. The recording box and

handle-bar potehtiometer could be easily removed and

replaced. Only the rear brake was retained because of the

bar potentiometer. The three speed gear could be altered

between runs but was normally set on low gear.

Removing the Cast(!)r & Gyroscopic Effects

The front forks of a normal bicycle are designed to

provide a measure of autostability. In order to ensure

that only the rider I s contribution to control was

recorded this stability had to be removed. Figure 5.1 and

the frontispiece

this aim.

show the alterations made to achieve

First the frame was altered to remove the rake from the

front wheel steering axis, bringing it into the

vertical. The forward throw of the axle was also removed

by mounting it on a bracket. The distance between the

88


ground contact points of the wheels was not altered but

the front

axis at

point now lay directly on

all steering and lean

the extended steering

angles. With this

configuration, side forces generated during steering no

longer produce a couple in the steering head. The

handle-bar remained in

front wheel via a short

its normal position

drag link. Jones

driving the

(1970) showed

that the front wheel of a bicycle acts like a gyroscope

during riding, precessing the steering into the fall and

providing a degree of autostability. When he constructed a

bicycle with a second front wheel alongside the first and

rotated it in the

much less stable in

opposite direction the bicycle was

roll. Jones' wheel was not driven but

spun-up by hand before the run.

Figure 5.1 The destabilized bicycle, showing the front forks (OFF) without castor, trail distance nor headrake. The destabilizing wheel (DWh) is driven in the opposite direction to the front road wheel which cancels the gyroscopic effect during rolling movements. This wheel is mass balanced by a counter weight (eW).

To remove the gyroscopic effect from the experimental

bicycle a second front wheel was mounted above the primary

wheel in such a way as to be driven in the reverse

89


direction but at the same speed. The tyre was removed so

that the grooved surface of the rim ran on the top of the

normal tyre and the rim was weighted to give it the same

mass distribution as the original. This arrangement put

the second wheel ahead of the centre of rotation so it was

balanced with a counter weight.

The Performance of the Zero Stability Bicycle

Although the extra wheel and the counter weight

obviously increased the inertia of the steering assembly

and the indirect operation made for a little more play

than normal, riding the Zero Stability Bicycle felt almost

exactly the same as riding the unmodified machine. This

was predictable since the autostability makes little

contribUtion to control at low riding speeds. The

steering felt light and well balanced, although the sight

of the large assembly moving during turns was a little

strange at first.

Two simple tests demonstrated that the autostability

had indeed gone. Like Jones' destabilized machines this

bike had no capacity to run on its own. If launched at a

good running speed it fell rapidly towards the side of the

first random displacement where the unmodified machine

would run on its own for several seconds. A pedestrian

pushing a normal bicycle can steer it by holding the

saddle and rolling the frame towards the desired direction

of turn. The destabilized bike could not be steered in

this manner as the wheel just kept pointing dead ahead no

matter what the operator did with the frame. It was not

possible to ride this bicycle 'no-hands', and it was

potentially dangerous as a road machine as there was no

natural tendency for the front-end to iron out sudden

directional disturbances caused by road bumps. Neither

experienced nor inexperienced riders had any difficulty

controlling this machine in ordinary manoeuvres at low

90


speeds, even when blindfold.

Subjects

The runs to which this section refers were made by two

subjects. Rider A was a male subject, age 52 years,

weight 178 1bs. He was an experienced bicycle rider in

good current practice. Rider B was also a male, age

34 years, weight 147 lbs. Rider B had been a regular rider

in his youth but had not ridden a bicycle much during the

five years preceding the experiments. The two riders' leg

lengths were sufficiently similar for them to use the same

seat pillar height. This put the riders' centre of mass

some 150 mm above the seat and slightly in front of it.

The scale drawing in appendix 1. (b) shows the calculation

for the combined centre of mass for rider and bicycle.

Despite the difference in weight between the two subjects

the two centres of mass are very close together being just

in front of the saddle peak.

Method of Operation

The runs were made on a calm dry day on a sand-surfaced

hockey pitch. A mobile laboratory containing the

microcomputer was positioned on the edge of the area near

to a mains plug on an electric sub-station. The

transmitter cable was pulled out to its full length to one

side and the rider positioned at a marked start point

heading on a course leading back down the wire. The runs

passed fairly close to the recording station and were

continued beyond it taking the wire out to the other side.

The experimenter stood within reach of the microcomputer.

When ready for the run to start he called for the

subject to start and pressed the start key as soon as

the rider was stable. The program shut down after

recording 750 data points in each channel, which at 30

msecs per point is 22.5 secs. The end was signalled by a

91


double beep and the experimenter called for the rider to

stop.

If it looked as though the rider would come to the end

of the wire before the automatic time was up the

run could be successfully terminated by pressing the

appropriate key. If the rider failed to stop then the

cable pulled out of its mounting without damage. The near

end of the wire was firmly anchored to prevent its

damaging the computer. Each recording period lasted

approximately 22 seconds, starting shortly after the rider

set off. All runs were started from the same place and

the approximate location where the recording terminated

was noted. Since speed was not regarded as a critical

value the approximate mean distance of the runs was

measured as 90 feet which gave an estimate of speed of 4

ft/sec Or just under 3 mph.

Blindfold Riding

At the start of the study it was evident that the

detection of roll rates is critical to the operation of

any control system. Since both the vestibular and visual

systems are capable of giving this information it was

decided to attempt blindfold riding during the recording

runs in order to reduce the number of sensory channels

being used. It turned out in practice that depriving the

rider of vision seemed to make little or no subjective

difference to the task, once the initial worry of riding

out of the prepared area was overcome. So far six people

have ridden blindfold. In each case the rider put on the

blindfold and went straight off without any difficulty.

In two cases, both children of ten, this first run was on

the destabilized model making the task that much more

exacting. Lack of time has prevented a more thorough

investigation to date, but the sureness with which all six

subjects tackled their first blindfold run argues for its

92


generality. All the runs relevant to this section were

made with the subjects blindfolded.

Instructions

The subjects were instructed to ride as slowly as

possible without falling off until told to stop. There

were two reasons for opting for the lowest possible speed.

The first the restriction of the transmitting cable and

the second was the need to get as much movement in the

traces as possible. The response from the tyre when

turned out of its true track, which provides the force for

turning and therefore correcting lean, is a function of

speed.

Thus at low speed more handle bar angle is needed for

any given lean effect. The subjects were instructed to

make no special attempt to maintain direction, the

intention being to stop the run if the limit of the

wire was reached or the run came too near to the recording

van. The reason behind this instruction was that,

combined with the lack of visual information, it was hoped

that no navigational control would be added to basic

stability control during the runs. However it transpired

that, despite this instruction, subjects tended to check

developing turns unintentionally so that the general

direction of the start was maintained for the rest of the

run.

Comparing the Channel Outputs

The raw data from both channels were digital records of

the voltage output from the transducers. The roll channel

was a record of rate of angular velocity at each sample

and the bar channel was a record of angular displacement.

The sample interval was 30 msecs between each channel

point. The BBC handbook warns that although the ADC reads

to 12 bits only 10 bit accuracy should be relied on.

93


Since all operations are carried out on the acceleration

information which has been smoothed twice by taking the

mean of seven local values each time it was not

considered necessary to convert the raw data. However

as a check the roll and bar values from a 600 point run

were compared with an 8 bit version. There were 264

differences out of 1200 points none of which was greater

than plus/minus 1. The bar channel lagged 15 msecs

behind the roll channel, this representing the time the

analogue digital converter takes to make a single

conversion and the program takes to store the value.

Therefore at zero LAG between the channels the bar channel

is lagging the roll channel by 15 msecs. When,

however, the handle bar data is differentiated the local

rate has been obtained by taking the change between the

target value and that value which immediately precedes it.

Consequently the differential value is in effect the mean

over the previous 30 msecs interval. The associated roll

value, which is a direct reading of angular velocity,

falls half way through this interval, with the result that

for the velocity and acceleration data the two sets of

readings are correctly synchronized and may be directly

compared without adjustment. To compare like with like

the following operations were performed.

The roll output was integrated to give roll angle.

Since the interest lay in relative changes this

integration was performed by summing the roll velocity

data without applying the time increment. This gave an

analogue of roll angle over time. During this operation

the curve was graphed so that a check could be made of the

zero position during the run. With straight runs the sum

of the roll velocities was near to zero over the total

time. Small adjustments of the DC constant value

accumulate to big changes in the final values so the zero

could be trimmed to a sUfficiently accurate figure where

94


there were any anomalies. This output was then paired with

the angle data of the bar channel. In graphical studies

the amplitudes were normalized to bring the curves

together. The horizontal scale in the angle graphs has

been adjusted to allow for the 15 msecs difference between

the channel recording points.

To provide

velocities the

a comparison between the roll and bar

bar output was differentiated by taking the

change over the preceding interval and noise removed by

taking the running average of seven local values. This was

then paired with the roll data. Again the time interval

factor was not applied and in graphical presentations the

amplitudes were normalized to bring them together. These

velocity values were differentiated once more and given a

further smoothing to provide a comparison between the

acceleration channels.

Although the main argument depends principally upon

operations to the angular acceleration channels a further

smoothing and differentiation was performed to produce the

third different ial of the angle, or jerk. Much of the

detailed information is lost in this operation due to the

extra smoothing which is necessary to remove noise. Peaks

are truncated and some smaller waves are lost but the

relationship between the general trends is much easier to

see in this filtered form.

The Recorded Runs

Appendix 2. (a) shows the plots of the roll angles and

handle bar angles for twelve blindfolded runs on the

destabilized bicycle by the two subjects. Runs 25 to 30

were by rider A and runs 31 to 36 by rider M. Appendix

2. (b) shows a limited section of each run giving the

angle, angular velocity, angular acceleration and jerk for

the roll and bar (dark lines) The full runs are given as

an indication that the selected portions are

95


representative of the whole. A limited section, 12 secs

of running time between point 100 and point 500, was

chosen for display so that the detail of the waves could

be more clearly seen. The start and finish of the runs

were avoided as there were possibly untypical readings

while the rider settled down to steady riding, or prepared

to stop as the wire was pulled out near to the full

length. The horizontal scale shows the recorded points

which are at 30 msecs intervals, thus the marked hundred

intervals are equivalent to 3 secs. The vertical scales

throughout have been adjusted by multiplication during the

graphing procedure to bring the peaks as near together as

possible for comparison between the rates of the two

channels.

RUN ROLL BAR

max min max min

25 0.93 -1.98 31.14 -50.52 26 1. 82 -1.21 38.11 -42.41 27 1. 27 -1.10 31.06 -47.25 28 3.66 -1.28 73.11 -22.64 29 1.0'7 -1.92 33.63 -50.28 30 2.05 -0.86 58.24 -31. 22 31 0.80 -1. 61 11.35 -46.97 32 0.66 -1. 95 14.59 -42.41 33 0.20 -1. 06 18.21 -27.72 34 0.57 -0.79 27.88 -27.28 35 1. 99 -0.68 35.98 -44.17 36 0.68 -1. 40 26.55 -47.59

Table 5.1 Maximum and m~nlmum angles of roll and bar in degrees for the destabilized runs 25 to 36.

The slow riding speed means that a large angle of

handle bar is needed to get an adequate response from the

tyres to control the roll and table 5.1 shows the maximum

and minimum angles of roll and bar used in these run

segments. It will be seen that none of the runs deviated

very much from upright running although large amounts of

96


handle bar were needed to achieve this. The roll angle was

calculated from the roll rate by assuming that the

velocities applied for the duration of the interval

between samples (30 msecs) in which each was recorded, and

the resulting angle increments summed for roll angle.

General Characteristics

The activity in the first three channels of a typical

run out of the twelve under investigation is reproduced in

figure 5.2 for easy reference. For exact detai Is the

appendix printouts should be studied as the reproduction

process introduces a small degree of distortion. All the

runs show the same general characteristic. In the angle

channel, shown on the first horizontal axis, it is

possible to make out an irregular slow wave from side to

side, assuming the convention that above the zero line is

left and below is right.

The ruh in figure 5.2 has about 7 reversals of

direction between data point 100 and data point 500, a

time of 12 seconds, giving a wave period of approximately

3.5 secs. Superimposed on this slow wave is a much shorter

one which is more clearly seen in the velocity and

acceleration channels. In the example there are something

in the order of thirty reversals of direction giving a

wave period of about 0.8 secs. It is not easy to arrive at

a simple criterion which will allow a cut and dried

decision as to what distinguishes a wave from noise but an

approximate 'eyeball' count of the half-waves of both

the long and short period movement in the twelve run is

given in table 5.2. The slower wave is taken from the

angle curves and the faster from the velocity curves. The

mean number of slow half-waves for the 12 runs is 5.7,

giving approximately 0.25 hertz and the mean for the fast

waves is 23 giving 1 hertz.

97


Run 33

Angleo. Roll and Bar (dark lineo)

Yeolocitlj. Roll and Bar (dark lineo)

Acceoleoration. Roll and Bar (dark line-)

Data Points

111111111111111111111111111111111111111

200 300 400

Figure 5.2 A typical section of slow straight line riding on the destabilized bicycle showing the activity in the first three channels. Reference should be made to the original computer printout in appendix 2, (b) for exact details as the copying process introduces a small amount of distortion.

The slow wave shows a tendency to a square shape with

fairly fast changes alternating with several seconds of

slow change while the differential waves have a triangular

Or • saw tooth' shape which is maintained to the third

derivative. This third derivative of angle or rate of

change of acceleration usually referred to as the jerk, is

98


shown on the fourth horizontal axis in the appendix

records but has not been reproduced in figure 5.2 to save

room. In the unsmoothed form the waves show the same

triangular shape as the preceding curves but are very

noisy. The smoothing process has flattened the peaks but

it is easier to see the time relationship between the

waves in this form.

Even before the relationship between the movement in

the roll and bar channels is analysed statistically quite

a lot about the nature of the control being used can be

gleaned from a simple inspection of the traces. When

'open-loop', that is when there is no control input at

all, the bicycle/rider unit will fall at an increasing

rate of acceleration until it hits the ground.

RUN big waves small waves small/big

25 5 20 0.250 26 4 20 0.200 27 4 22 0.182 28 4 21 0.190 29 3 22 0.091 30 5 19 0.263 31 7 32 0.219 32 7 26 0.269 33 6 30 0.200 34 5 26 0.192 35 9 21 0.429 36 10 22 0.455

Means 5.7 23.4

Table 5.2 The approximate number of large and small half-waves counted between points 100 and 500 in the destabilized runs 25 to 36 with the ratio of small to big waves in the third column. See text for details.

This basic response is shown in the computer

simulation record in the upper half of figure 4.4. Because

the moment arm of the disturbing couple is constantly

99


changing with the angle of lean this roll movement can

only be bought to rest by a controlling response which is

able to alter at exactly the same rate and exactly

synchronized in time. If the control system cannot achieve

this, then the next best thing is to alter at the same

rate but at some phase delay. During the delay the control

will be locally inappropriate, but providing the phase

shift is short compared to the natural frequency of

response, it will give stable control, although the nature

of the movement will be oscillatory. If the system cannot

continuously change at the same rate as the disturbing

couple the only means of control left is to change in

discrete steps. Here, at best, the controlling value will

be correct once during a discrete interval as the

disturbing couple passes through that value.

Continuous traces of the changes taking place in the

disturbing and cohtrolling couples will immediately reveal

which class of control is being used. If a discrete steps

are being used then one of the derivitive curves will show

the handle bar -trace moving in square steps while the

associated roll trace moves in a non-linear curve. That is

during the discrete interval the bar produces a fixed

acceleration or a fixed velocity while the roll angle, in

its response to the constantly changing moment arm, will

be following a changing one.

It is evident from the traces that a discrete steps are

not being used to control the roll angle and this is

confirmed later in this chapter where it is shown that the

movemeht in the bar has a very high correlation with the

local movement in the roll, but not with its own previous

movement which it obviously would have if it was using a

'ballistic' type of standard acceleration rate rather than

following the changes in roll. It is also evident that a

very short phase lag!follow system is not in use since the

acceleration is not damped down to nothing. This leaves

100


the continuous follow at some moderate delay and it can

easily be seen that in all four derivitives a great deal

of the bar change is a delayed repeat of the movement in

the roll channel. The phase delay varies both between runs

and within runs but a study of the zero crossing points

shows that in run 33 in figure 5.2 the delay appears to

vary between a quarter and a half of one of the ten data

point intervals, that is between 75 and 150 msecs.

The Similarity Between the Roll and Bar Traces.

An inspection of the records for these runs shows that

the rate of movement of the handle bar is following that

of the roll at some fairly consistent time delay. The

next task is to find out how closely they are matched

and what exactly the delay is between them. It is useful

to bear in mind at this point that, with the autostability

removed from the bicycle, all movements in the handle bar

are due entirely to movements of the rider. If the rider

were to let go of the handle bar the steering would remain

at its last angle. If, as is apparent, the handle bar is

following the acceleration changes of the roll then the

rider must be making it do so.

Cross Correlation Function (CCF)

The first test of similarity between the two curves

also provides information about the delay between them.

The CCF carries out a Pearson product-moment correlation

on two columns of time series data. At each pass it varies

the 'lag' between the two columns. So for instance if a

range of lag values up to 10 was being examined, the first

pass pairs the tenth value in the first column with the

first value in the second column, then the eleventh with

the second and so on. The second pass takes the ninth with

the first and the eighth with the second and so on. This

yields a series of correlation coefficients from lag

101


values of -10 to +10. If there is a similarity in the

rate of change in the two columns at some lag value the

correlation will jump to a high figure at that lag with

high correlations at the nearest lag values either side.

section Pr lag section Pr lag R sqr

RUN 1 2 3 4 5 6 7

25 100-700 .69 4 200-400 .91 4 64.9 26 100-700 .66 4 " .65 5 73.9 27 150-700 .63 4 " .64 4 74.9 26 100-700 .63 4 " .63 3 71. 1 29 100-700 .62 3 " .63 2 69.1 30 250-650 .60 4 300-500 .62 3 70.1 31 100-700 .66 2 100-300 .69 2 61. 6 32 100-700 .90 2 " .93 2 66.9 33 100-700 .64 2 " .91 2 66.6 34 100-700 .90 3 " .66 3 67.3 35 100-700 .62 3 " .67 3 76.5 36 100-700 .67 3 " .69 3 79.7

Table 5.3 Showing the correlations and lags between the roll and handle bar angular accelerations for the twelve destabilized runs (25-36) between the points indicated in column 1. See text for further details.

Short lengths of totally uncorrelated data or large

changes in phase within an otherwise highly correlated

set have a disruptive effect on the final correlation

value. Column 1 in table 5.3 shows the section of the

total ruh used to obtain the correlations in the following

column. For all but two runs the central 600 points,

representing 18 secs of running time, were used. The start

and finish sections were discarded for the reasons already

given. Run 27 and run 30 gave correlations below 0.7

for the 100-700 section and an exploration showed a sharp

increase for the more limited sections indicated so these

were used. The CCF is performed on the smoothed

acceleration data of the roll and bar channels. Limited

102


sections of these data are displayed in the graphs in

appendix 2, (b). Column 2 of table 5.3 shows the Pearson

product-moment correlation coefficient obtained for each

run and col. 3 shows the lag value at which this high

figure appeared. The critical value at 0.01 probability

level even for the short set of 400 points at a lag of 50

is 0.14, so it can be seen that these correlations are all

highly statistically significant.

The MICROTAB statistical package running on a BBC B.

microcomputer was used for subsequent operations and

limited memory forced a further reduction of the data

sample to 200 points. Column 4 Table 5.3 shows the

sections selected for each run. Run 30 again proved more

choosey than its predecessors and the sample was shifted

to get a slightly better correlation. The similarity

between the correlations and lags obtained with CCFs in

the short sections and those from the full run may be

checked by comparing the values in columns 5 & 6 with

those in 2 & 3. The correlations are of the same order

but the differences in lag for rider A (runs 25 to 30)

suggest that this value is not fixed but varies to some

extent within a run. A closer look at this point will be

taken later when an alternative method of measuring lag

has been introduced.

Whether the peaks of high correlation are isolated or

appear at regular lag intervals depends on the exact

differences between the waves being considered. In the

case of exactly similar waves with constant wave-lengths

and peak a~plitudes then groups of alternatively positive

and negatitre high correlations will appear at half-wave

periods. The lag values at which the maximum peaks appear

give the phase difference between the waves. If there are

differences in wave shape within similar wave lengths,

such as a sine-wave versus a more triangular wave then the

same regular peaks of high correlations will appear but

103


the peak values will be lower, reflecting the differences

in local amplitudes. In the case of exactly similar sets

of values where the wave-length and/or amplitude varies

throughout the length of the run, then the CCF gives a

much more 'focussed' response. With regular wave-length

but varying amplitude from wave to wave there is a sharp

focus of peak correlation at the critical lag value. The

positive and negative peaks still appear at half-wave

intervals but their peak correlations are much lower than

that at the correct lag value. When the wave-length

varies then the secondary peaks tend to disappear and the

peak of high correlations is confined to the critical lag

value.

totals RUN order + - zero-wave - + cols

3-7

1 2 3 4 5 6 7 8

25 1 .4 .6 .91 .5 .4 19 33 2 .4 .7 .91 .5 .3 19 32 3 .2 .6 .93 .4 .2 14 36 4 .2 .6 .89 .3 .3 14 27 5 .3 .5 .84 .4 .2 14 26 6 .3 .4 .85 .3 .3 13 34 7 .2 .6 .86 .4 0 12 28 8 .2 .5 .83 .3 .1 11 35 9 0 .6 .87 .2 0 8 31 10 0 .5 .89 .2 0 7 30 11 0 .5 .82 .1 0 6 29 12 .1 0 .83 .1 .1 3

Table 5.4 The peak correlation values either side of the absolute peak value from table 5.3, cols. 5 & 6 at half wave intervals. Thus cols. 3 & 4 are the correlations found at a full wave and one half wave preceding the peak wave respectively, and 6 & 7 are those following it. Col. 8 shows the total values of the subsidiary wave peaks (Cols. 3-7) on which the runs have been ordered. Col. 5 is correct to 2 significant figures the other columns are corrected to 1 place of decimals.

104


A CCF analysis was performed for the indicated sections

of each run for a range of 24 lag values either side of

zero. The results are summarized in table 5.4. The ZERO

WAVE at column 5 shows the peak correlation obtained at

the lag value given in column 6 of table 5.3. On either

side of this are the peak values at the nearest half-wave

positions. These are given simply to 1 place of decimals

so that the eye can more easily pick out those runs which

show little evidence of peaks either side of the critical

value. The secondary peak values are summed in column 8.

These have been used to list the runs in descending order

of subsidiary peak strength. There are approximately 12

half-waves in each of the six-second run sections. From

the appearance of the CCF output it is possible to deduce

that about one third of the runs had fairly constant

half-wave periods over the six seconds run with

differences in amplitude accounting for the reduction in

correlation; a third had a good deal of disruption in

the wave period length which suppressed the secondary

waves and the final third lay somewhere between.

It looks from table 5.4 as though there is a tendency

for high correlations to be associated with high secondary

peak values. Columns 5 and 8 show a 0.616 correlation

which is significant to P<. 05 (Critical value for 10 df

0.576). The critical variables which affect the

correlation between two similar wave forms may be

considered as having two components. The first is the rate

of change of amplitude within a wave period, and the

second the half-wave period length. Since the CCF

printouts, summarized in table 5.4, show that half the

runs have considerable differences in wavelength within

the 12 secs run the question that arises is whether it is

this factor which also causes the extra reduction in peak

correlation or whether there is some unidentified factor

which affects both the wave-length and the overall

105


correlation at the same time. In order to answer this it

is necessary to examine the effects of distortions in

amplitude and wave-length upon correlations in some more

detail

Effect of Amplitude and Wave-length

It is evident that two wave forms must be very similar

to obtain correlations in the order of 0.8. It is also

evident that the final figure is a consequence of the

relationship between the two values at each time point.

It would however by useful to have some general idea of

how amplitude and wave-length, as defined in the previous

paragraph, affect the final correlation.

1. Amplitude. If it assumed that there is a perfectly

consistent wave-length throughout both sets of data then

it is evident that the maximum distortion to amplitude

that cart occur within a half-wave is that one set of

values is at zero and the other somewhere near the

maximum. The following table shows the reduction in

correlation between sets of data as a result of flattening

part of one of them. The basic wave is a sine function

with 100 max. amplitude, ten 360 degree waves with a

sample rate of 18 degrees, giving 200 points. This gives

approximately 10 points to each half-wave. The second

wave is progressively flattened by setting the indicated

points at zero. The R squared term from a regression

prediction of one set of values from the other is a more

sensitive measure of similarity than correlation so both

measures are shown.

Degree of flattening Correln Regress

R sqrd

1/2 wave (1 to 10 to zero) 0.975 95.1%

3/4 wave (1 to 15 to zero) 0.952 90.6%

1 wave (1 to 20 to zero) 0.945 89.4%

106

Bicycle Riding

2 waves (1 to 36 to zero)

3 waves (1 to 55 to zero)

0.894

0.836

Chapter 5

79.9%

69.9%

This is a straight line function and does not depend

on the absolute number of waves present but the proportion

which are 'flattened'. In general terms if three out of

ten waves are at the maximum amplitude difference then a

perfect correlation will be reduced to just over 0.800.

In the case under examination the maximum correlation is

0.91 and this drops to a minimum of .83, which is the

equivalent in the table above to the difference between 2

and 3 waves set to zero, that is a change of 1/10 of total

waves. It is therefore evident that quite large

differences in wave area would be needed to account for a

reduction of this magnitude if the amplitude differences

were the only factor affecting it. Actual differences in

wave area will be dealt with shortly.

2. Wave-length. The reason that amplitude does not

have a large effect on the overall correlation is that the

disruption is confined to the locality of the associated

wave. When there are differences in wave-length, the

location of the disruption makes a big difference to the

resulting correlation. To unpack this effect the same wave

form used for the amplitude test was altered as follows;

the values in the second set of data were phase delayed by

an increasing number of degrees. For each delay value the

consequence on the correlation for the number of waves so

affected was measured. Thus if there is a phase change of

20 degrees in the fifth wave (out of a total of ten) then

half the wa~es are phase shifted 20 degrees from the other

half. If on the other hand only the last wave in the run

is shifted 20 degrees the distortion is confined to this

one position. A phase shift of 40 degrees (approximately

a fifth of a half-wave) even if applied over the maximum

of half the run only reduces the correlation to appx.

107


0.94. However a shift of 180 degrees when applied over

half the run gives half at a correlation of 1.0 and half

at -1.0, and therefore gives a correlation of O. In effect

the correlation process sets the whole run at 90 degree

phase lag which gives a zero correlation. As the change

is moved down the run the consequences are mitigated but

are still strong. Just one wave 180 degrees (half a

wave) out of phase at the end of a run of ten waves will

reduce an otherwise perfect correlation to 0.8. Shortly

these differences will be examined in detail but in the

meantime a close examination of the acceleration curves

for the runs in appendix 2, (b) show that there are

frequent phase changes of about a quarter the mean

wave-length, and occasional examples of half-wave

length phase shifts. (Run 25, 450-460; run 29, 150-160;

run 30, 345-355; run 35, 390-410). Of course just how

much phase shift there is also depends on the mean lag

taken for the section of run in question and the

relationship between lag and wave-length will also be

dealt with in a later section. It is however evident that

a badly placed phase shift of this sort is sufficient to

account for the lowering of correlations noted when

selecting data runs for examination.

A more detailed discussion must be delayed until the

method of extracting a measure of wave-length and area has

been introduced. However the data summarized in table 5.4

suggests that the amplitude values are well coordinated

over time, that is the areas under the curves are closely

matched, giving a high correlation between the two wave

forms at the appropriate lag value. When the wave lengths

within the run are consistent then this leads to the high

secondary peaks at half-wave intervals shown in rows 1 to

4 of the table. When there are differences in the

wavelengths within the run the peak correlations are

reduced and the secondary peaks are suppressed. Therefore

108


the expectation is that areas should show a greater

correlation between roll and bar than wave lengths and

that where there are large reductions of correlation

between roll and bar in a section of run this is due to

differences between the wavelength rather than amplitude.

Regression Analysis

To examine more closely the relationship between the

roll and bar movement a regression analysis was performed

on the acceleration data to see to what degree the roll

values predicted the bar values. For all subsequent

regressions the sections of data from point 200 to 400

were used for each run. There was considerable variation

in the lag values between runs and possibly within them as

well. The lag value from the CCF analysis, shown in

column 6 of table 5.3 was used to locate the regression

analysis. This procedure uses the equation:-

Predicted Value = Constant + (multiplier * Predictor value)

to predict a set of values from the roll data. It then

compares the predictions with the bar values at the

appropriate delay. In a series of reiterations it alters

the two injected values until the best fit is obtained.

Column 7 in Table 5.3 shows the R squared term, which

being the square of the correlation coefficient times 100,

is a measure of how well the final regression equation

fits the overall data. The minimum F value for the run

was 452. The degrees of freedom are 1 and 196 and the

critical F value for 200 degrees of freedom at a

significance of p<.OOl is 11.17. All the 't' values for

the acceleration term were in excess of 20 and the

critical value for p<.OOl for a df of 120 is 3.37. It can

be seen that the observed level of association between the

109


two sets of values at the given lag is very highly

statistically significant.

Thus the analysis so far has shown that the basic form

of the rider response on the destabilized bicycle was a

close imitation of the roll rate at a mean delay between

120 to 60 msecs. The next phase in the analysis will be

to focus on the local changes in wave-lengths, delay, and

area under the curve for each wave within the runs to see

if there are any further invariant relationships in the

data.

WAVE PERIOD, AREA AND DELAY ANALYSIS

Introduction

The analysis so far has shown that the movement in the

bar acceleration channel is closely related and dependent

upon the movement in the associated roll channel. Although

the CCF analysis gives a mean delay between the channels

it is evident frdm an inspection of the graphs that there

are considerable changes in both wave period and delay

both between and within the runs. It is obvious from the

high correlations obtained that the areas under each

individual wave must be closely matched but here again

there are obvious differences. In order to find out more

about these differences a program was written which

extracted wave periods, areas and delays for the runs.

Matching the Roll and Bar Waves

The following operations were carried out on the roll

and bar acceleration waves between points 100 and 700.

Throughout the discussion the word 'wave' is used to mean

a half-wave in the convention of an alternating positive,

negative wave form.

Wave Period. The roll and bar records were each treated

as follows. The next zero crossing and direction was

110


identified by its point number. A search was made for the

next zero crossing and the interval in points constituted

the wave period interval which for simplicity will now be

termed the wave length.

Wave Area The values of the points within a wave were

summed to give a value which is a direct analogue of the

area under the curve.

Delay. Each roll wave was matched with the next bar

wave of the same sign. Occasionally one of the waves fails

to cross the zero line at its lowest point and is

consequently missed by the search process. This leads to

an artificially long delay period. Any delay greater than

10 data points was discarded. If the bar wave recrossed

the zero line within the next roll wave then one reading

was lost, and if the bar wave failed to recross the zero

line at all then two were lost.

RUN 25 26 27 28 29 30 31 32 33 34 35 36

All 45 43 46 53 53 46 57 57 61 59 59 58

l1atch'd 42 40 37 42 42 38 49 52 55 53 40 50

Prop .93 .93 .8 .79 .79 .82 .86 .9 . 9 . 89 . 68 . 86

Table 5.5 Showing the number of matched waves found in the destabilized runs (25-36, points 100-700). The last row shows the proportion of matched to total waves. See text for further details.

Table 5.5 shows the proportion of waves which were

successfully matched using this criterion. There were

slight discrepancies between roll and bar totals as an

occasional wave will just fail to cross the zero line but

these were not thought to be of importance and the total

111


wave figure refers to roll waves only. From this it was

concluded that the matched waves were representative of

the activity in the two channels and the analysis

proceeded on these waves.

Internal Consistency

The first question to be answered is how consistent are

the measures within the runs. Table 5.6 shows the mean

values for wave, area and lag for the 12 runs. (cols.

1,3,5,6,9) .

wave-period wave-area 1ag

RUNS roll bar roll bar

1 2 3 4 5 6 7 6 9 10

25 14 4B 12 4B 122 77 115 BO 4.5 4B 26 14 42 13 4B 120 67 9B BO 4.0 62 27 15 37 13 49 146 63 13B 75 4.1 51 2B 13 35 12 40 112 5B 109 63 4.0 52 29 13 44 12 42 96 70 B6 74 3.6 57 30 14 3B 13 46 106 70 101 64 4.3 53 31 14 53 10 46 115 72 79 67 2.9 54 32 11 42 10 40 105 65 B6 66 2.9 41 33 11 44 10 44 103 92 90 77 2.9 45 34 10 3B 10 36 105 66 104 66 3.6 3B 35 13 39 12 56 141 73 132 Bl 4.1 4B 36 11 42 11 43 117 72 100 71 3.9 4B

means 13 42 11 45 116 70 103 72 3.7 50

Table 5.6 Showing the values and variability for the half-wave periods, wave areas and lags for the 12 destabilized runs 25-36 (points 100-500). The even columns show the coefficient of variation (stand. dev./mean * 100) for the value in the preceding (odd) column. Each value is the mean for the run. All but column 9 are corrected to the nearest whole number. Column 9 is corrected to 1 place of decimals.

The even numbered columns show the coefficients of

variation. This is the standard deviation divided by

the run mean and, being independent of the absolute

112


values, may be used to compare the amount of variability

for all measures. These values should be read in

conjunction with the histograms of the actual scores given

in appendix 2, (c) .

Waves Areas Autocorrelation roll/bar roll/bar Bar Bar Roll

Corrn. sig Corrn. sig. wave a.rea. area

RUN 1 2 3 4 5 6 7

25 .44 .01 .80 .01 ns .62 .42 26 .37 .05 .85 .49 .37 27 .38 .05 .54 ns .57 28 .56 .01 .63 .34 ns 29 .42 .80 ns .46 30 .84 .69 .43 .37 31 .71 .80 ns .31 32 .72 .80 ns .36 33 .82 .90 .35 .53 .50 34 .51 .82 " .55 .48 35 .44 .74 " .46 .44 36 .48 .82 " ns ns

means .p6 .77

Table 5.7 Showing the roll/bar correlations and autocorrelations for wave-period and area. Columns 2 & 4 show the significance level for the correlation in the preceding column. In columns 5-7 the coefficient is shown only if it is significant at better than the P<.05 level.

Because of the row limit in MTAB these have been shown

separately for the two individual riders but they give a

clear illustration of the point that the wavelengths are

much closer to the means than the areas which have a

square distribution. This is reflected in the coefficient

of variance being nearly double for the latter. The lag

shows a similar characteristic to the wavelength.

113


Relationship Between Roll and Bar

Since the correlations and regressions have shown that

there is a close relationship between the roll and bar

movement the next question is how the local changes in

wavelength and area are correlated between the roll and

bar.

Table 5.7 shows that there are significant correlations

between both sets of values but that the area is the more

closely correlated of the two. Thus a situation exists in

which there is a tendency for the wavelength to vary to a

lesser degree about a single value but when changes do

occur they are only moderately correlated between the roll

and bar channels, (col. 1).

The areas of successive waves on the other hand show

almost twice as much variation as the wavelength and

have a square shaped distribution showing that anyone of

the range of values is as likely to appear as another. As

these changes take place they are highly correlated

between the roll and bar. Column 3 shows that 8 out of the

12 runs have a correlation of over 0.8 with a mean for all

areas and many

followed by a

runs of 0.77. Thus there are many small

large areas and a small tends to be

matching small and a large by a large. Wavelengths tend

to vary about one size and where there are differences

a small one is less frequently followed by another small

one. The delay between the channels also shows a tendency

to be distributed around a single value and the variation

is of the same order as the wavelength. The mean values of

lag extracted by the measuring process for each run can be

checked against the lags resulting from the CCF analysis

by comparing column 9, table 5.6 with column 3, table 5.3.

In general the former are slightly higher than the latter

but it should be borne in mind that they are measured

exclusively at the zero crossing position whereas the CCF

114


is taking the best interval for all parts of the curve.

Because the minimum interval is 30 msecs this is in any

case a rather coarse measure, giving discrete jumps to

represent a process that must certainly be continuous.

The only dimension the rider can alter is the rate of

bar movement. However the way in which it is altered can

take several forms. First the length of the delay between

the sensed roll rate and the bar rate output can alter.

Rapid changes in the delay are bound to lead to local

changes in wavelength. The amount of response, or gain,

can be altered. If the rate is held at zero for example

for a short time then there will be associated changes in

the local wavelength which will lead to changes in delay

measured at the zero crossing points. The same thing will

happen if the gain is rapidly increased or decreased and

very similar effects will follow the superimposition of

bar rates that are independent of the basic follow rate.

A more detailed analysis of whether these changes are

noise caused by the system's inability to sustain a

constant value for lag or gain and how they affect the

characteristic follows in the next chapter. However one

more question can be answered at this stage and that is

whether there are any signs of these changes being

ballistic in nature.

Evidence for Ballistic Control

The recorded roll and bar rates show that the system

is operating continuously and not in discrete steps.

However it might be asked whether it produces, for

example, a standard wavelength or delay which achieves a

partial solution to the immediate control problem and then

gradually shifts this value on the basis of feedback of

errors between the desired state and the state actually

achieved. If any of the values showed this sort of change

then there would be an autocorrelation with neighbouring

115


values within the run.

The autocorrelation process performs a series of

correlations between a time series and the same series

shifted by a lag value. The first pass compares point 1

with point 2, point 2 with point 3 etc. The second pass

compares 1 with point 3 and 2 with 4. If there is any

tendency in the run for neighbouring values to be more

like each other than more remote values the correlation

will be high at a lag value of 1 and perhaps 2.

The delay value can be dismissed quickly as there were

no significant correlations between one value and

neighbouring values up to a lag of 8 for any of the 12

runs. Column 5 of table 5.7 shows that there was only one

significant correlation at a lag of 1 for the bar

wavelengths and none at a 1ag of 2. Thus it is clear that

there is no 'ballistic' tendency in the wavelength.

Column 6 shows that 7 of the 12 runs showed a moderate

degree of correlation between immediate neighbouring

values (lag of 1) of the bar areas. There were no

significant correlations for the second lag position.

Since the bar area is highly correlated with roll area

(Col. 3) it would be expected that when for some external

reason two adjacent roll areas are similar then the bar

area would show the same tendency. Of the seven runs with

a significant correlation at 1 lag, six show a significant

correlation at 1 lag in the roll data. It can be

concluded that

unlikely in

any sort of ballistic control is very

the bar area since five runs showed no

similarity in adjacent values but displayed general

characteristics of control no different from the other

seven runs. Since run 28 showed a significant correlation

in the bar area at 1 lag without there being a similar

correlation in the roll area the appearance of such a

correlation cannot be due exclusively to the observed

tendency for the bar area to copy the roll area. In

116


general it appears that the dynamics of the system as a

whole are such that there is a tendency for roll areas to

show some degree of autocorrelation and that since the bar

area is closely associated with the roll area this is

reflected by a lesser degree of autocorrelation in the bar

areas.

Summary of Basic Run Output

Two subjects rode the destabilized bicycle,

blindfolded, for six runs each of just over 20 seconds.

Although instructed not to correct for any turns they did

in fact keep the bicycle oscillating about the upright,

reversing incipient falls about once every two seconds.

This was not achieved smoothly as there was a short wave

oscillation of roll of about 1 hertz. Because of the low

speed large amounts of bar movement were needed to control

the roll but the analysis is concerned with the rates of

change rather than absolute values. Because all

autostability had been removed from the bicycle all the

bar movement must have been due solely to rider response.

The form of this response was a close imitation of the

roll rate at a delay which varied from 4 to 2 data

points (120 to 60 msecs), measured by the mean delay given

in the CCF analysis. A regression analysis showed that

from 70% to 86% of the bar movement was accounted for by

the movement in the roll channel. The 1 hertz wave

component was isolated in the acceleration waves at the

zero crossing points and waves with same signs matched.

Each pair of waves yielded measures of lag/delay, local

half-wavelength period and area under the curve. Lag and

wavelength showed a coefficient of variation of 40/50

about a mean value with the roll and bar channels

correlating at about the 0.55 level. The areas on the

other hand showed a coefficient of variation of 70 with a

fairly even distribution between the maximum and minimum

117


values. The matched wave areas showed a correlation at

about the 0.77 level. It was evident that the system was

detecting the roll changes continuously not at discrete

intervals and there was no tendency for the bar responses

to be 'ballistic'.

The first part of the analysis has shown that, although

each run had a completely different sequence of values in

the two channels, an invariant relationship between the

activity in the roll and bar rates existed. The handle bar

angle responded continuously to the changes in roll rate,

which since the riders were blindfolded must have

originated in the vestibular system. The delay between

detection and response was considerably faster than that

traditionally associated with central decision making and

is therefore in the range associated with the functional

stretch reflex. The next stage will be to find how such a

response affects the performance of the rider/machine and

whether that part of the bar activity which is not

accounted for by the roll activity is noise or some

additional means of control.

118


6. SIMULATING THE DESTABILIZED BICYCLE CONTROL

Testing the Implied Control System

In the previous chapter it was discovered that a large

part of the activity in the handle bar acceleration

channel during normal straight running on the bicycle was

accounted for by the movement taking place in the roll

acceleration channel some 100 msecs earlier. The next step

in the analysis is to put this kind of control into the

simulation to see what performance characteristic results.

This output will be compared with that of the actual runs

and modifications sought which will bring the two nearer

together. The final aim will be to try to construct a

control system for the model which gives an output with

the same characteristic as that of a real rider over a

comparative run time.

The General Response to Delay/Follow control

Moving the bar to the left forces a roll to the right

so that a rising roll value is suppressed by the rising

bar that follows it at the lag interval. It can thus be

appreciated that the effect of the delay in the bar leads

to a situation at every peak where the bar is still

increasing even though the roll has already been forced to

reverse. During this interval the bar, having checked the

roll increase in the initial direction, is now driving it

the opposite way. Thus when the bar follows the roll at a

delay there are two opposite effects. It reduces the roll

acceleration when it is in the same direction and

increases it when it is in the opposite direction. Which

of these effects dominates depends on the combination of

two factors, first the length of the delay and second the

degree to which the bar value responds to the roll value.

If the delay is very short indeed then the bar movement is

almost all used in containing the roll and the roll

119


divergences are damped out rapidly to zero. In this case

the higher the multiplication factor the quicker the

damping. The limit case in the opposite direction is

when the delay is as long as the time taken for the

bicycle to fall all the way to the ground, say 2 seconds.

In this situation the bar movement would fail to reduce

the roll at all, regardless of the mUltiplication factor.

However there is in practice a much shorter limit period.

Even if the delay is substantially less than that

given above and the bar movement manages to contain the

fall by virtue of a high multiplication factor, this same

high factor will then force the roll in the opposite

direction during the lag period. On the reverse it will be

faced with a much worse condition as the bicycle will now

be falling the other way at a speed that is the

combination of both the gravity effect and the velocity it

acquired during the reverse thrust.

Consequently it can be seen that with a lag/follow

system the gaih factor must be matched to the delay

period so that with a long delay a high gain does not

drive the system into diverging

also an absolute upper limit for

oscillations. There is

lag where even a weak

gain factor will fail to reverse a roll divergence. There

must also be some minimum delay period that is dictated by

the time taken for the physiological mechanism to extract

the information, process it, transmit it to the operating

muscles and for those muscles to respond. In the

previous chapter the lag for the two riders, measured at

the zero line; was seen to vary about a mean of

approximately 100 msecs with occasional values near to

zero or greater than 200 msecs. The first question to be

answered is what is the general response characteristic of

the simulated bicycle to variations in lag and gain in a

delay/follow system.

120


Stability

The output of a system proposed for the rider/bicycle

combination has two principal parts, one a steady state

component directly related to the input and the other made

up of transient terms which are either exponential or

oscillatory with an envelope of exponential form.

time

(8) ( b)

(c) o (d) (e) Figure 6.1 The feedback control actual value and

five kinds of stability common to systems. The difference between the the desired value is used to drive

the initial disturbance back to the zero line. The ratio of the control force to the damping dictates whether the system is stable or unstable.

(a) Under-damped; stable oscillatory. (b) Under-damped; unstable oscillatory. (c) Under-damped; 'just stable'. (d) Over damped. (e) Critical damping.

Damping in the system suppresses these transient

effects and the way it behaves as a result is described as

follows. If the exponentials decay to zero the system is

said to be stable. If any exponential increases, the

system is said to be unstable and a theoretically 'just

stable' system shows a sinusoidal oscillation with a

stable amplitude. Figures 6.1, (a), (b) & (c) show an

121


example of each case. If these transients are too

heavily damped the steady state component may fail to

reach the controlling value in which case the system is

said to be overdamped. When the damping is such that the

new value is reached rapidly without oscillation the

system is said to be critically damped. Figures 6.1, (d) &

(e) show these last two conditions. Since the term

'critically damped' has a precise definition the term

'dead-beat' will be used to describe a condition which

nearly approaches the critical state. Appendix 3, (a) shows

the four main cases on the simulator using the

destabilized Triumph with a 160lb rider at 4 mph using the

delayed roll/follow control with a lag of 120 msecs.

Although only the repeat of the roll acceleration has been

discussed so far the latter part of this chapter has been

anticipated in constructing these diagrams in that the bar

channel is a repeat of a combination of both the

acceleration and velocity roll channels for reasons which

will shortly become evident.

It would be convenient at this stage to have some

quantitative measure of stability with which to describe

the effects of gain and lag. The normal engineering

control procedure for describing the stability and the

suitability of proposed control for a system is to work

from the op~n-Ioop data to the closed-loop performance.

The open-loop equation of the system in the Laplace form

is graphed on a Nyquist diagram which plots the real terms

on the X axis and the imaginary on the Y axis. From this

diagram it is possible to predict what time and gain

constants will produce a stable closed-loop system.

The quantitative measures of stability are the gain and

phase margin which are defined as follows

(Healey,1967,pages 102-117)

Gain margin. That increase in open-loop gain which

gives an overall gain at 180 degrees phase shift of unity.

122


At this point the system is on the verge of instability. A

negative gain margin indicates an unstable system.

su.

600

500

400

300

200 over,.. damped Fails to reaoh oontrol value too stable

100

critical.l.:r S'fA.BILI'fY da.ped

D

e

B

A.

just stahl.e

Destabilised Tri\lJl\ph

Normal Corsair

u nde r - da m I!ed Diverging osoillatory unstable

Figure 6.2 The upper and lower stability limits for two different 1bicycles' running on the simulator. The dark lines show the gain settings associated with these two points for the Triumph 20 destabilized machine at 200,150,100 and 50 msecs lag, identified by the dark lines A,B,e and D respectively. The same points for the Carlton Corsair tourer are shown by the light lines a,b,c and d. The speed is 4 mph and the rider dimensions 6ft and 5 slugs (16Ubs).

Phase margin. That phase lag required to put the

system on the verge of instability with the existing gain

value. If the system is already unstable this value will

be negative. In the absence of open-loop data no single

quantitative measure for the stability can be given.

However an idea of the stability performance of the total

system running with the repeat/delay control can be

obtained by identifying the two points where the system

changes characteristic from underdamped to over-damped and

123


from stable oscillatory to unstable oscillatory for a

range of the critical variables gain and lag. Figure 6.2

shows in graphic form these two points for a range of gain

and lag values.The function of the stability between these

points is continuous and would appear on a Nyquist diagram

as a spiral. Because no values for the stability are

available here the two points are merely joined with a

straight line to aid identification. The two boundary

conditions were obtained by gradually increasing the gain

setting until the trace showed the required

characteristic. For the 'Critical damping' case (Appendix

3, (a), first figure) the gain setting was that which

.caused the velocity trace (R') to just reach the Y=O axis

but not cross it. For the 'Just stable' case (Appendix

3, (a), third figure) the gain setting was that which gave

no change in amplitude (measured in the acceleration

channel, R") over time.

The two points enclose the range of useful stability.

For any given lag when the gain is low the stability is

good but the power to control disturbances is poor. As

the gain is increased to give more power the system

approaches the point of unstable diverging oscillation.

When the lag is long only small gain values are possible,

and as the lag gets shorter so more and more gain can be

used without sending the system into the unstable range.

The lag and gain are the critical variables for any

given system, other variables having little effect on the

stability performance. Different bicycles constitute

different systems with different stability

characteristics. To illustrate this point the stability

range for two machines is shown. The dark lines show the

stability for the Triumph experimental bicycle and the

light lines the stability of a large wheeled touring

bicycle (Carlton Corsair). The bicycle speed and rider

dimensions are the same in both cases. It is evident that

124


the design of the tourer is superior to the small wheel

utility machine allowing more gain to be used for the same

lag.

Changes of non-critical values within a single system

do not have

this point

(weight and

much effect on the stability. To illustrate

the effect of a range of rider dimensions

for the two

height) and road speeds

stability points for

on the gain

the Triumph

running at 100 msecs lag are shown:-

Speed 4 mph. Lag 100 msces.

Wt Ht Stability Gain stones ft

18 6 Critical 100

Just stable 265

11 6 Critical 100

Just stable 265

5 4 Critical 110

Just stable 200

settings

bicycle

Table 6.1 The effect of rider weight and height on the upper and lower stability boundaries. Taken from runs on the simulated destabilized bicycle.

It can be seen from this table that large changes in

rider weight and size have very little effect on the

stability boundaries of the system. As already mentioned

in chapter five the response from the tyres which

provides the controlling couple is a frictional force

which is dependent on the weight. The heavier the rider

the more power per angle of drag is available for

countering the weight disturbance so there is in fact not

a great deal of difference in the amount of gain

between light and heavy riders. However, even

125

required

if this


were not so, it would not change the stability boundaries.

It would merely mean that, for a given lag, a heavy rider

would reach the diverging oscillatory condition sooner

than a light rider, not that the threshold was different.

Rider 11 stone 6ft. Lag 100 m.secs

Speed Stability Gain m.ph

2 Critical 110 Just stable 275




Table 6.2 The effect of speed on the upper and lower stability boundaries. Taken from runs on the simulated destabilized bicycle.

The response from the tyres is dependent on speed. Thus

more tyre/road angle is needed to counter a given lean

angle as the speed decreases which means that mOre gain is

needed for a fixed lag when manoeuvring at low speed.

However the gain margins are not much changed by speed

so that the system will be more oscillatory at low speed

because it is forced to operate at a higher gain setting

and thus nearer the 'just stable' boundary and not because

the stability characteristic has altered.

Power for Control and Wavelength.

In general the greater the gain the greater is the

instability and the lower the gain the lower is the power

of response. All control systems are a compromise between

126


these two opposing requirements. There are two unstable

conditions, one when the gain is so low that the system

cannot correct a disturbance and the other when the gain

is so high that the system takes on a diverging

oscillation. Regardless of where the stability margins lie

the control needs the power to deal with disturbances and

this is a function of absolute gain. As the angle of lean

increases so does the disturbing couple and the rate of

fall increases exponentially. The correcting couple must

accelerate faster in order to contain it and the absolute

value of the gain is the critical value which dictates its

power to do so regardless of the ratio of gain to lag

Disturbance 5 deg. initial lean

Ge.ih Lag Angle where fall checks

100 (60,120,200) Failed to check fall

140 60 11 degs. 120 11 degs. 200 13 degs.

Disturbance 15 deg. initial lean

140 (60,120,200) Failed to check fall

200 60 25 degs 120 26 degs 200 35 degs

Table 6.3 Showing how the power to check an initial disturbance depends principally on the gain. Figures taken from a run on the simulated destabilized bicycle with an 11 stone rider at 4 mph.

Table 6.3 shows the effect of different absolute gain

settings on the ability to reverse an initial disturbance

for a range of lag values. The the roll error, times the

gain factor is applied to the handle bar at the phase

127


shift indicated by the lag value. The angle where the fall

checks is the roll angle at which the fall due to the

initial lean angle was checked and reversed. It is

apparent that the performance is not entirely independent

of the lag value. The longer the lag the later the

steering sets off in pursuit so even though it is growing

at the same multiplication factor as the short lag case it

has a more difficult task to start with. This accounts for

the reduced performance in the 200 msecs lag case. All the

recorded runs showed variations in the wave period.

Gain Lag Wave-period

(lIIsecs) (secs)

100 100,120 2.5

120 " 1. 9

130 " 1.6

140 " 1.5

200 " 1.0 (1. 3)

280 " 0.7 (0.9)

400 " 0.5

Table 6.4 The effect of gain on wave-period during the recovery from the disturbance due to an initial lean angle of 5 degrees. Simulation of the destabilized bicycle with an 11 stone rider at 4 mph. See text for comments on 1ag effects and figures in brackets.

The time taken to reverse a disturbance is a function

of the gain for any given lag. Consequently the wave

period in a

gain. Table

during the

series of reversals is also a function of

6.4 shows how the period of the oscillations

recovery from an initial disturbance of 5

degrees lean varies with different gain values.The gain

128


is the critical variable controlling the wave period but

once again lag has a small effect. The periods for the

above table were measured by counting the number of waves

on the screen and then noting the time elapsed during

their formation. However for short lags the lower gain

settings produce an almost dead-beat performance and it

was not really possible to do more than make a rough

estimate of where the only wave terminated, thus the

figures given are those for lags of 100 and 120 msecs.

The figures for lags of 60 and 200 agreed where they could

be measured with slight increases in the shorter wave

periods for lag 200 as indicated in brackets.

Summary of Laq/Follow General Characteristics

A repeat of the roll activity in the bar acceleration

channel at some delay is capable of containing

disturbances introduced into the system. The success in

containing these depends on two main factors. First the

gain must be high enough for the bar response to catch and

reverse the roll rate before the angle of lean gets too

high and second the ratio of gain to lag must not get so

high that the system becomes unstable. It has also been

shown that changes in gain lead to substantial changes in

wave period whereas changes in lag have only a marginal

influence. Table 6.S summarizes the various effects of

lag and gain. The heavily outlined boxes show the range of

gain values which give a stable performance for the three

lag values, ranging from unstable due to too little power

at one end to diverging oscillation at the other.

It is evident from the traces in appendix 2, (b) that,

whatever the reasons, the control system in the 12 test

runs is near the lag/gain ratio for the 'just stable'

condition since there is more sign of incipient divergent

instability than dead-beat critical damping. It should not

be expected that the simulator model can make precise

129


quantitative predictions about the detailed performance of

the actual bicycle since a number of the variables

are only approximately defined, particularly the way

the tyre coefficient varies with speed and angle. However

the observed mean wave period of I hertz and lag of 100

msecs with a high degree of oscillation ties in well with

the computer predictions. The 120 msecs lag gives a 0.9

wave period when the gain is such as to put it on the

'just stable' limit. This setting gives plenty of power to

deal with quite large disturbances.

Since the delay between sensing a change of roll and

implementing a change of bar is a sum of various internal

processes it is very unlikely that the value would be

absolutely stable. However this noise alone will not

account for the changes in wave period as we have seen

that the influence of lag on its own is weak. There is a

0.45 correlation between the lag and the roll wave period

for 11 of the 12 runs, indicating that changes in one are

connected with changes in the other. It is obvious that

whenever the wave period changes, there is a transient and

quite strong effect on the local lag value as measured at

the zero-crossing point. A sudden reduction in the wave

period will also shorten one or two lag values at the site

of change. It seems likely therefore that the changes

observed in the lag value are caused by both noise due to

instability and changes in the wave period, with the

latter being the stronger effect.

It seems clear from the behaviour of the simulator so

far is that there is no need for constant change in the

gain when riding the bike in a straight line with low lean

angles. Running as it is around 100 msecs lag with a gain

setting high enough to put it in the stable oscillating

condition it has more than enough power to deal with the

disturbing couple of the weight.

130


Lag Gain Characteristic Disturbance (degs)

2 5 15

200 80 Overdalllped nc nc nc

90 Stable dead-beat 12.8 nc nc

120 Stable Osc. 5.8 16.5 nc

130 just stable 5.7 14.5 nc

140 Unstable Osc. 5.3 13.4 nc

200 Unstable Osc. 4.5 10.7 35.0


90 Stable dead-beat 12.0 nc nc

140 Stable Osc. 4.2 11. 0 nc

200 Stable Osc. 3.0 8.0 26

240 just stable 3.0 7.4 23

280 Unstable Osc. 2.8 7.0


140 Stable dead-beat 4.2 11. 0 nc

200 Stal:Jle dead-beat. 2.8 7.5 25

280 Stable Osc. 2.6 6.5 20

350 Stable Osc. 2. 5 6. 0 18

170 just stable 2.3 5.5 17

500 Unstable Osc. 2.2 5.5 17

Table 6.5 The effect of gain and lag on stability. Lag in ffisecs, gain in nominal units and figs. in cols 1-3 in degrees. See text for details.

131

Wave period (secs)

-2.5

1.9

1.6

1.5

1.3

-2.6

1.5

1.0

0.9

0.7

-

-1.0

0.6

0.56

0.5

0.4


Control, however, has a problem in establishing just

what that gain setting should be, as differences in speed

affect the balance between the response from the tyre on

the road, which is speed dependent, and the weight couple,

which is not. The tyre response is a value which will also

change considerably between different bicycles and on

different road surfaces and it is not parsimonious to

propose that the rider carries a variety of settings in

memory from which the appropriate value is selected as a

result of sensing the critical variables which affect it.

The Cross-Over model of operator performance of McRuer and

Krendal which resulted from a study of a selection of

compensatory tracking tasks (Summary in Smiley, Reid &

Fraser, 1980) showed that operators adjusted the gain

factor to allow for different system delays, thus

demonstrating that humans are able to alter gain for

control purposes. The simplest solution to the gain

problem would be to try some default value and observe the

response. If this is too low then the gain is turned up

and if too high it is reduced. At the start of a run it is

obvious that the setting will always be high to cope with

the low speed and a large error in initial selection could

be safely corrected by putting a foot back down on the

ground. The result of such a procedure is bound to be

considerable variation in the gain setting during a run

especially since the system prefers to operate with a high

gain putting it near the 'just stable' boundary. Thus,

since wave period is dependent on gain, it can be argued

that at least some of the wave period changes are due to

this cause. Bar movements not connected with the

roll/follow response will also change both period and lag

but whether there is some as yet unidentified additional

input producing this effect must wait until the

characteristic has been analysed to a greater depth.

132

Bicycle Riding

Ti

"

~

Lag

Chapter 6

Ro I I Ue I .

,,-"" Bar "-Roll Reel.

Figure 6.3 Illustrating how the values in the roll velocity channel vary compared with those in the acceleration channel at a sample point shown by the line Ti. The Bar channel is shown as a repeat of the roll acceleration at a delay marked as I Lag T. See text for other details.

Acceleration and Velocity

When the regression analysis was performed on the roll

and bar data in the previous chapter it was assumed that

the roll acceleration information was the only ingredient

being used by the system to modify the bar output.

Control systems however may utilize various forms of the

basic input to achieve different results. Figure 6.3

shows a formalized representation of the roll acceleration

and velocity waves and the bar acceleration wave following

the roll acceleration at a delay labelled LAG. If it is

assumed that the bar value is a repetition of the roll

acceleration then the relevant value associated with the

bar value A is marked at B. At this point the associated

roll velocity value is at C. Because the velocity curve

runs 90 degrees behind the acceleration curve it shows a

maximum value here as opposed to the acceleration value B,

which is zero. Thus the control system could increase its

133


response at low

velocity as well.

acceleration values by adding in the

was at a maximum

Obviously when the acceleration value

the velocity would be making no

contribution. In practice the velocity value could be

obtained from the acceleration by integrating

successive values which is the sort of operation a neural

circuit is well able to perform. In the next section the

effect of using either the acceleration or a combination

of acceleration and velocity on the characteristic will be

explored.

Assume first that the control is only responding to the

acceleration value. When there is a disturbance either

from road irregularities, side winds or a stray

uncoordinated movement by the rider, an acceleration in

roll will result. Since there is a delay in responding,

velocity of roll will accumulate during the interval

between the start of the disturbance and the response

which checks the acceleration. Even when the acceleration

has been removed the velocity will remain and the lean

will continue to ihcrease at a steady angular velocity.

In practice, since the increasing angle of lean will

give an increase in disturbing couple, the acceleration

will start again without any external encouragement and

the process will be repeated with more velocity

accumulating. Figure 6.4 illustrates this sequence on the

computer model running at 4 mph with a lag of 120 msecs

and a gain setting of 240. The bar acceleration is a

repeat of the roll acceleration only.

134

Bicycle Riding

S,"cs BIKE..£ 4

R ( 2)

mph S

(2)

Gain 240 R""

( 7)

<::

Lag 120 S""

(15)

Chapter 6

R" (3)

Figure 6.4 Delay control on roll acceleration only. In this and the following three figures the disturbance is a symmetrical on/off push of 600 msecs rising to a maximum by half-way. The start is marked by an arrow which shows the direction of the effect on the roll acceleration (RI I). The figure at the top of the left axis (4) shows the nominal strength of this push.

From the exact upright position a small disturbing

pulse is introduced. It can be seen that the roll

acceleration (R") is rapidly contained and oscillates

about a mean value that is itself moving slowly left. This

drift is quite clear in the velocity channel, R'. The

velocity that was introduced during the disturbance

remains, so the angle of lean, R, keeps increasing. The

velocity itself increases as well because of the imbalance

between the disturbing and correcting couples with

increasing lean angle.

If the control is now altered to feed both roll

acceleration, R", and velocity, R', into the bar response

the characteristic alters as shown in figure 6.5. Here the

bar is responding to the accumulated velocity value as

well as the acceleration and the former is gradually

reduced to zero in three or four oscillations. However the

135


angle which also accumulated during this operation is not

removed as can be seen by the resulting lean, R. In

general terms the velocity and acceleration introduced by

the disturbance are removed by turning the bicycle into

the lean until the centrifugal force balances the

displaced weight couple.

Secs BIKE..£ 4

R mph S

(2)

Gain 200 R"

Lag 120 S" R'

(3) ( 2)

4

.1

Figure 6.5 (R I , ) arid

reduced to velocity. figure 6.4.

(15)

Delay control on roll acceleration velocity (R'). The gain has been allow for the additional effect of All other values are the same as in

Velocity Contributions in the Recorded Runs

Since the velocity curves (appendix 2, (b)) can be seen

generally to return to the zero line from each wave

excursion they seem to suggest that some velocity

information is being fed back into the bar movement. In

order to test this a multiple regression was run

predicting the bar acceleration values from both roll

acceleration and roll velocity values. Columns 1 and 2 in

table 6.6 show a comparison between the R squared values

for this regression and those from the previous regression

using acceleration data alone. Column 3 shows the

136


significance levels for the multiple regression. All the

acceleration terms remain very highly significant and only

one of the velocity terms falls below p<.OOl to p<.OS.

(Run 28). Again the F numbers for the goodness of fit of

the regression are all well over the critical value for

p<. 001. In every case the R squared value rises, the

actual differences are shown in column 4 with a mean

difference of 3. From this it may be concluded that the

combination of roll acceleration and roll velocity provide

a better prediction of the bar acceleration movement than

the acceleration on its own. In this section of some of

the runs, 32,33 and 34, the combination is accounting for

90% of the bar movement, which when allowance is made for

noise and external disturbances is very high indeed.

This evidence supports the idea that the main influence

on the bar movement is a continuous repeat of the activity

in the roll channel sensed as both changes in acceleration

and changes in velocity. The delay between the two

channels is not absolutely constant but is sufficiently so

to yield very high correlations when a mean value is

used. There are differences between the run sections

analysed here.

correlate at

The R

0.74

squared

with

values for these sections

the original Pearson's

product-moment coefficient values for the whole runs shown

in column 2 of table 6.3. This is an indication that some

runs have more extraneous movement in them than others but

it will be shown shortly that there are also considerable

differences of this sort within quite short sections of

the runs. It will be argued later that this irregularity

is a consequence of one of the essential control features.

Attempts to control using velocity on its own are not

successful because in effect it is the same as increasing

the length of the delay by a quarter of a phase, which

with a basic wave-period of about 1 secs means a minimum

delay of 250 msecs plus any further transmission lag.

137


Section 200-400 Section 200-370 Col Col

accl accllvel 2-1 accl/vel plus angle 7-5 RUN 1 2 3 4 5 6 7 8 9

25 85 87 .001 2 89 .001 89 .001 0 .001 .001 .001

ns 26 74 76 .001 2 76 .001 77 .001 1

.001 .001 .001 ns

27 75 77 .001 2 71 .001 71 .001 0 .001 .001 .001

ns

28 71 73 .001 2 70 .001 71 .001 1 .05 ns .05

ns 29 69 73 .001 4 73 .001 74 .001 1

.001 .001 .001 ns

30 70 74 .001 4 67 .001 67 .001 0 .001 .001 .001

ns

31 82 83 .001 1 83 .001 83 .001 0 .001 .001 .001

ns 32 87 91 .001 4 91 .001 91 .001 0

.001 .001 .001 ns

33 87 90 .001 3 89 .001 89 .001 0

.001 .001 .001 .01-

34 87 89 .001 2 89 .001 90 .001 1 .001 .001 .001

ns

35 78 84 .001 6 84 .001 84 .001 0 .001 .001 .001

ns

36 80 85 .001 5 85 .001 85 .001 0 .001 .001 .001

.01-m.ean 3 0.3

Table 6.6 The R squared terms & significance of the predictors for a series of multiple regressions predicting bar from roll. See text for details.

138


An examination of the upper and lower stability limits

using the same procedure as that applied to the model of

the destabilized Triumph which provided the values for

figure 6.2 using velocity information only shows that the

system is inoperable with such a long delay. There is no

critically stable point since a gain setting which is low

enough to prevent oscillation provides so little power

that the front wheel reaches a critical value before the

fall is contained. If the gain is increased sufficiently

to contain the fall by a reasonable lean angle the system

is so underdamped that it goes out of control before the

second reversal can take place.

Secs

..

J

BIKE..J: 4 R

( 2)

...... ....... ........

mph S

(2)

....

Gain 240 R""

(7)

Lag 120 S""

(15) R"

(3)

Figure 6.6 Delay control on roll velocity (R') only. The gain has been increased slightly to balance out the loss of the acceleration contribution, other values as in the previous three figures.

To provide a comparison with control using acceleration

feedback this condition is illustrated in figure 6.6.

Removing the acceleration contribution reduces the overall

gain so this has been slightly increased to put the first

reversal

quarter

angle on the screen.

phase behind that

The velocity

of the

growth runs a

acceleration,

consequently the gain drives the roll a long way after the

reverse before the velocity value rises far enough to

139


check it. The initial fall is reversed after about 6

degrees but the control is so slow in building up that the

lean has reached 19 degrees to the right and the roll

acceleration has only just reversed. Since there will be

a further delay before the roll velocity reverses there is

no chance of recovery before the lean angle becomes

excessive.

Absolute Angle as an Input Variable

If the control is using only acceleration and velocity,

as described above, the response to a disturbance would be

a stable turn. However if the next disturbance happened

to be on the same side then a further increase in lean

and turn would result and there would be nothing to

prevent excessive angles accumulating after a period of

running. Thus otherwise undirected runs would be expected

to show considerable changes of direction and occasionally

loss of control. In order to keep a constant mean heading

the control must respond to the angle as well. It is

evident from the fact that the subjects kept an

approximately straight course during the runs, even though

they had been instructed not to bother, that the riders

did react to the lean angle or to the rate of turn

which will always accompany lean when under control.

Therefore the next question that arises is whether to go a

step further and include the lean angle R in the bar

response so that the lean angle is also removed, returning

the machine to upright running following a disturbance.

Figure 6.7 shows that the system is well able to

accommodate such a modification. Here the roll angle R

has also been added to the bar response. The increasing

lean, R, acting through the bar rate, forces the velocity,

R', further to the right than in the previous two runs

which in turn brings the lean back gradually to zero in a

series of gentle oscillations and the machine resumes

140


straight upright running. A bicycle controlled in this way

would maintain a straight upright course, gradually

removing any lean angles that accumulated as a result of

external disturbances, which is exactly what happens with

motor-cycles and bicycles at speed.

Secs

.I.

BIKE...c 4 R

( 2)

mph S

(2)

Gain 200 R"

( 7)

Lag 120 s"

(15)

Figure 6.7 Delay control on roll acceleration velocity (R') and absolute roll angle (R). values as in the previous three figures.

R' (3)

(R I , ) I

Other

Evidence Against continuous Angle Control

The appearance of the roll angle traces in the

destabilized runs does not seem consistent with the smooth

removal of lean angle illustrated in the computer

simulation of figure 6.7. Although all the runs maintain

a mean of zero there are constant excursions either side

forming the observed 0.25 hertz wave. In order to test

whether angle was also being used by the delay/follow

system a multiple regression was performed predicting bar

response from acceleration, velocity and angle data. Due

to lack of memory space

the run points had to

in the statistical routine some of

be discarded. The regression is

performed on the first 170 points of the 200 point run

used for the previous regressions, that is points 200 to

370. Column 5 in table 6.6 shows the regression for the

141


two predictors, acceleration and velocity, for the

shorter sections so that it may be compared directly with

column 7 which is the regression for the three predictors,

acceleration, velocity and angle. It will be seen that

removing the last thirty points has revealed some local

differences within the runs but the significance of the

predictors remains above the p<.OOl level except for the

velocity contribution to run 28 which has fallen below the

significance level. The reliability of the R squared

prediction remains well above the p<.OOl level throughout.

Although the reliability of the R squared prediction

remains at the same high level for the three predictors,

column 8 shows that only 4 of the angle contributions are

significant, 3 at p<.Ol and 1 at p<.05. Of these, two at

the p<.Ol level are negative sign which means that to

obtain the overall fit on these runs the angle component

was being subtracted not added. This of course is a bigger

argument against its being a regular contributor than its

being not significant. The other two predictors remain at

a high level of significance with the same sign. Column 9

shows that the change in R squared brought about by adding

the angle term is much less than the change produced by

adding the velocity term shown in column 4 but where it

exists it is always positive.

There is no evidence to support the proposition that

the angle term is used continuously in establishing the

bar movement. However, where the angle term is significant

the correlation improves so it is possible that angle is

being added discontinuously with its sign independent of

the other two continuous contributors. That is there are

irregular short pushes which may work either against the

roll or with it.

142


The Discontinuous Application of Roll Angle

If the underlying control is a delayed repeat of the

roll acceleration and velocity in the bar acceleration on

which some form of angle control is intermittently

superimposed then one would expect the prediction of bar

from roll acceleration and velocity to show similar

discontinuities. The regression analysis gives the

residual values, which are the differences between the

predicted value and the actual value at each data point.

If those which exceed the 95% value (1.96 of the standard

deviation from the mean) are plotted, short runs of

disruption over several adjacent values are revealed. Two

short sections of 50 data points each were selected from

each run, one which included such an area of disruption

and one which did not. The terms 'clear' and 'disrupted'

will be used to distinguish between the two types of run.

Table 6.7 shows the clear sections selected in column 1

and the disrupted sections in column 6. Two clear sections

(Runs 32 and 33) were shorter than 50 to prevent the

inclusion of a disrupted section. The other columns show

the results of regression analyses first with acceleration

and velocity as predictors and then with angle added.

Columns 4 and 9 show the significance level and direction

of the three predictors and columns 5 and 10 show the

change in R squared value which resulted from the addition

of the angle factor.

Throughout all runs the significance of the R squared

term remained well clear of the p<. 001 level. No F

distribution term fell below 100 with a critical value of

11. Some runs showed no increase of R with the addition

of the angle term, some showed a considerable increase and

none showed a reduction. There was slightly more change,

measured by the means, in the disrupted areas but the

distribution of the contributions shows quite a marked

143

Bicycle Riding

RUN

25

26

27

28

29

30

31

32

33

34

35

36

Chapter 6

Clear Section Disrupted Seotion

1 2 3 4 5 6 7 8 9 10

3251 96 96 .001 0 265} 89 89 .001 0 375 .001 0 315 .001

ns ns 230} 87 90 .001 3 260} 62 64 .001 2 280 ns 310 ns

.01- ns 250} 58 68 .001 10 290} 83 94 .001 11 300 ns 340 .001

.001 .001-300} 68 79 .001 11 230} 81 89 .001 8 350 ns 280 .001-

.001 .001

200} 87 87 .001 0 250} 87 87 .001 0 250 .05 300 .001

ns ns 300} 89 90 .001 1 210} 76 83 .001 7 350 .001 260 .001

ns .001-230} 97 97 .001 0 300} 83 87 .001 4 290 .001 350 .001

ns .001 250} 97 99 .001 2 290} 88 89 .001 1 290 ns 340 .001 .. ,", .001- .05-

2tO} 97 97 .001 0 345} 93 93 .001 0 , I ,~

295 ns 395 .001 ns ns

2'66J 96 96 .001 0 200} 85 88 .001 3 :i1ci .001 250 .01

.05- .01 2dO} 82 83 .001 1 345} 85 86 .001 1 , 0 25 ns 395 .001

. ns ns-320} 91 91 .001 0 250} 87 93 .001 6 370 ns 290 .001

ns .001-mean 3.2 3.6

Table 6.7 Comparing the R squared term from regressions predicting bar acceleration from roll in two sections, one disrupted and one clear f from each of 12 runs. See text for details.

144


difference. Most of the change in the clear runs comes

from two high values in runs 27 and 28. These two runs

also show another difference in that their starting R

values are much lower than the other ten. If these two

runs are excluded then the mean changes become 0.6 for the

clear runs against 2.49 for the disrupted runs which is

consistent with the view that the angle term is having

little effect in the clear sections but is contributing to

the bar acceleration movement in the disrupted sections.

All the acceleration terms remained very highly

signific'nt and positive in sign. Although the velocity

term was highly significant in all but one of the

disrupted runs, five in the clear runs were not

significant, though two of them were in the p<.l bracket.

All remained positive. The contribution of the velocity

term to the regression equation is much smaller than that

of the acceleratibn (means over 20 regressions: velocity

factor 0.030, acceleration fa'ctor 0.834). A possible

explanation of this difference between the clear sections

and the disrupted sections is that there is very little

velocity present in the short clear sections so the

contribution locally falls below significance. An

examination of the traces in appendix 2, (b) is not very

encouraging to this view although it is difficult to make

a clear judgement without some specific criterion.

If it is supposed that the acceleration output from the

semi-circuiar canals is integrated by some neural process

to obtain velocity then such a process is likely to take

some time and may be partly discrete or have some

threshold value below which is does not operate. This

could lead to the more definite appearance of velocity in

the disrupted sections if the disruptions are associated

with more roll movement.

An interesting result is the effect on the significance

levels and signs of the angle predictor. Table 6.8 shows a

145


levels and signs of the angle predictor. Table 6.8 shows a

surnmary:-

Significance Clear Disrupted

NS (p>.l) 7 4

NS (p<. 1 ) 1

S (p<.05) l(neg) l(neg)

S (p<.Ol) 1 (neg) 1

S (p< .. OOl) 3(2 neg) 5(3 neg)

Table 6.8 Showing how well the roll angle predicted the rate of bar change in a clear section and a disrupted section of 12 runs (see text for definitions). Significance of the angle predictor term from the regression is in the left hand column and the number of incidences in either condition for each level is shown in the next two columns.

Since only one significant positive value for angle is

found in the clear runs it is evident that this

information was not making a continuous contribution to

the bar acceleration values. Of the 7 significant

contributions to the disrupted runs four are negative so

it is clear that although there was a contribution from

some source which correlated highly with the amount of

lean angle present, it was not consistently applied in

relation to the existing direction of lean. It should be

borne in mind here that over 50 data points, about 1.5

secs, there is frequently very little change in the lean

angle (~ppendix 2, (b)) so that the contribution to the

regressions for this term is more in the form of a

constant term rather than a variable.

146


Intermittent Control

It seems quite certain from what has been found so far

that the roll acceleration continuously dictates the major

part of the relationship between roll and bar, with a

smaller addition from the roll velocity. Extra movement,

which seems to be correlated with the absolute angle of

lean, is superimposed on this base from time to time. The

disrupted sections analysed in the previous section were

chosen from the excessive regression residuals. To get a

better picture of what these disruptions looked like for a

complete run a routine was written which applied the

multiplication factors for roll acceleration and velocity

found in the regression performed on points 200-400 (Table

6.6, column 2) to the 100-500 sections of the runs shown

in the graphs in appendix 2, (b). Those residuals which

exceeded the 95% threshold were plotted to give the graphs

in appendix 3, (b). A study of these plots shows that the

same general characteristic is to be found for all runs.

There are large sections with residuals below the

threshold and occasional localized sections of 10 to 15

points where the values accelerate to a central peak value

and then fall back again. Sometimes the peaks are isolated

and sometimes they appear close together with the sign

alternating.

The Simulation of Intermittent Peak Inputs

The next thing to discover was the effect on the

characteristic when an intermittent peak input was

superimposed on the continuous activity of the

acceleration/velocity follow/delay system. To simulate

this situation a routine was written which added a given

force to the handle bar by increasing it in equal

increments over a set period and then reducing it to zero

in an equal number of steps. The peak value and period of

147


application could be altered at will. The general

response of the characteristic to these inputs was the

same regardless of these two values.

BIKE..£ 4 mph Secs R S

(3) ( 3)

5 (

7 ..

I

BIKE..£ 4 mph Secs R S

( 3) (3)

iD

1

~ 2 , , c.:. 5 .; ..

" 3 l )

r :"':' , )

f . <"

J. )

I < ..

Gain 200 R"

(25)

Gain 200 R"

(25)

c ::;, <;.:

-~

'-:-

.. '. .~

Lag 120 S"

(60)

Lag 120 S"

(60)

-:':

+-

::> ,

R' (5)

R' (5)

r

Figures 6.8 (a) (upper) & (b) (lower). The effect of pushes of various lengths applied to the simulated bicycle under roll/follow control. The initial disturbance is 2 degs. lean left. The push duration in (a) is 1200 msecs and in (b) is 600 msecs. The arrows show the start of each push.

A push produced a roll in the direction of application.

When the push ceased the underlying roll/bar follow

control removed the acceleration and velocity and left the

148


machine in a stable condition with the accumulated lean

angle remaining as already demonstrated. The amount of

lean change that resulted was a function of the amount of

power applied. That is, a long weak push equated to a

short strong one, however as will now be shown the

characteristic of response did alter with duration of

push.

Figure 6.8 shows the effect on the characteristic of

the simulated bicycle. The values used are the same as

those used in the previous demonstrations. The lag was set

at 120 msecs and the gain at 200 to put the system near

the 'just stable' condition so that there would be plenty

of movement. The machine starts off with a 2 degree lean

to the left. Once the underlying roll/follow control has

removed the disturbance and the bicycle is steady in a

turn to the left a push is applied to force it to the

right. The point at which the push is applied is shown in

the figures by an arrow indicating the direction of

effect on the acceleration trace (R"). Once the lean has

reversed to the right another push is made to force it

back to the left again. The strength of the push (shown

in nominal units to the left of the R axis at the top) is

adjusted with the length of the pulse to give the same

amount of push in each case. Figure 6.8, (a) shows the

effect of a 1200 msecs push of nominal value 5, (b) shows

a 600 msecs push of 10 and (c) a 300 msecs push of 20.

One of the most interesting differences between the

push effects is the behaviour of the velocity channel.

Long pushes force the mean velocity curve away from the

zero for several half-wave periods. One wave is well clear

of the zero, that is it fails to make the zero crossing

and the general displacement of the trace during the large

angle movement is evident to the eye. The 1200 msecs

period is equal to nearly three half-wave periods and the

oscillations in the angle channel are suppressed during

149


the change. As the period of application gets shorter the

displacement of the velocity trace gets less as the main

part of the movement takes place within one half-wave

period (600 msecs is somewhere near the half-wave period

and 300 msecs is well within it). with the shorter pushes

the short wave movement is evident in the angle traces, R

and S, which is also a feature of the real traces in

appendix 2, (a) and appendix 2, (b) .

Secs

:1.0

r.

5

"I

3

:z

I

BIKE..c 4 R

( 3)

-. ') <: , '.., •

,.

~

~

Gain 200 tag 120 R" S" R'

(25) (60) (5)

...... --:;:;,

~ . c:,_ ........

:::~

<. f-<_ -.:;~,

~ c.-:;:--'

< Figures 6.8 (c). The push duration is 300 msecs; all other values as in previous two figures.

Evidence for the Push in the Traces

If it is proposed that part of the control system

consists in imposing short pushes onto the underlying

roll/follow control then it appears from the above that if

the pushes were substantially longer than the half-wave

period of 500 msecs then there would be a large number of

incidents where the velocity wave failed to make the zero

crossing and these would be associated with the pushes.

Although it is difficult to define an exact criterion for

a failure to make a zero crossing since the local

wavelengths show variation, the following table shows an

150


approximation of such occurrences.

Run Detached Location Excessive waves (data pt) Residuals

25 1 330 7 26 0 - 10 27 1 275 3 28 2 280.350 5 29 3 260.320.440 6 30 1 460 15 31 3 310.325.460 4 32 3 200.280.460 7 33 1 425 10 34 4 200.295.370.415 7 35 2 270.380 8 36 7 165.250.310.345 etc. 5

Table 6.9 Showing the number of roll velocity waves which failed to make a zero crossing in the 12 runs and the number of pushes unassociated with roll movement in each run as indicated by the excessive residuals from the regression analysis. Whether the velocity trace crossed the zero line or not was judged by visual inspection and the location of each point is shown in column 2.

The final column shows the number of excessive residual

peaks recorded in each run. There is obviously no reason

for supposing that, if the excessive residual activity is

a place where a directing push is applied, this leads to

the velocity wave failing to cross the zero line. Thus it

can be argued that if pushes are being applied at these

locations they must be shorter than a half-wave. This view

is further endorsed by the fact that none of the excessive

residual runs are longer than 10 points, or 300 msecs.

Attention will now be concentrated on the section of

run 33 from point 350 to 450. Figure 6.9 reproduces the

roll and bar movement graphs from appendix 2, (b) and the

regression residuals from appendix 3, (b) on the same

page to assist in following the argument.

151

Bicycle Riding

Run 33

Angle_ Roll and Bar (dark line)

Yelocit" _ Roll and Bar (dark line)

Acceleration_ Roll and Bar (dark line) \

Regression Residuals greater than t _96 SD_

Data Points

Chapter 6

1

V

111111111111111111111111111111111111111

200 300 400 ::;

Figure 6.9 The first three channels from run 33 in appendix 2, (b) show~ in relation to the excess regression residuals for this run from appendix 3, (b) .

152


The convention applies that movement upwards is to the

left and downwards is to the right. At point 360 the roll

angle (faint line in the top graph) makes a rapid

excursion to the right (down) This is reversed at 390 and

there is a rapid movement to the left which is checked

just after 410 from whence the movement becomes more

gentle. Turning to the regression residuals at the foot of

the page it will be seen that a left bar movement in

excess of that predicted from the roll and velocity

movement is located between 360 and 370.

At point 360 ih the acceleration graph there is a bar

r~sponse (dark line) to the left (up) well in excess of

the roll acceleration. A glance to the earlier part of the

acceleration trace will show that up to this point the bar

peaks more or less match the roll peaks. (The immediately

preceding lower wave which also has an excess peak with an

associated residual peak is ignored at present to keep the

argument simpler). The result of this extra acceleration

in the bar drives the roll velocity response to the right

(graph immediately above) so that it diverges from the bar

velocity. The excess acceleration in the bar is reflected

in the jerk trace by a steeper slope between 355 and 365

(from appendix 2, (b). The jerk trace has been left out of

figure 6.9. ) Despite the extra left bar input the

underlying roll/follow mechanism eventually predominates

as the push declines after its peak value at 365 and the

bar acceleration pursues the roll acceleration to the

right (down).

There is no excess push between 360 and 370 and the

roll/follow movement of the bar succeeds in reversing the

right going roll acceleration just before 370. Even

though the roll has been reversed the bar continues to

accelerate to the right for the delay period (about 100

msecs or a third of one of the marked intervals) thus

153


driving the roll more strongly to the left back towards

the zero line. However at 380 a further small left bar

residual excess appears so this movement is somewhat

inhibited giving the rounded curve in the reverse of the

roll velocity at 380 to 385. At just under 385 a very

strong right bar residual excess appears so that the bar

acceleration which has just begun to pursue the rising

roll acceleration is severely truncated between 385 and

400. This leads to an exaggerated roll velocity peak which

is reflected in the large left roll angle movement back

across the zero line in the upper graph.

By 400 the control, no doubt unwilling to leave the

recovery entirely to the underlying roll/follow system,

puts in two successive excess residual peaks at 405 and

410 to assist in containing the left roll. These have the

effect of holding the bar acceleration on the left side

between 400 and 410 thus driving the roll acceleration to

a very exaggerated right peak at 415 which ties in with

the reduction in the big roll velocity bulge between 390

and 415 and with the termination of the big left roll

movement between the same points in the upper graph.

The above section was chosen for examination because it

was the most exaggerated push in the sample. Equivalent

corresponding movements in the angle, velocity,

acceleration and jerk traces can be seen at the locations

of the other larger excess residuals but are more

difficult to follow as their size diminishes. The exact

shape of the trace which results from such additions

depends on where the push falls in relation to the

existing wave.

Figure 6.10 shows how a small wave adds to a big one

to produce a modification in shape that depends on their

phase relationship. The section of run 33 analysed above

gives good examples of both in-phase and out-of-phase

additions. The downward peak at 350 coincides with the

154


down going acceleration wave and exaggerates its movement

without distorting its shape. The next upward peak does

the same. The small upward push at 385 is in opposition to

the existing wave and cuts its top off with some

distortion. The large peak at 390 is also opposing the

acceleration wave and also distorts its quite badly. Run

27 shows an in-phase addition at point 305 and there are

other examples of both in and out-of-phase distortions

elsewhere, though not always accompanied by excess

residuals.

Figure 6.10 The effect of phase change on the appearance of a wave. The small triangular wave is added to the continuous saw-toothed sine-wave at an increasing phase interval to give the dark wave shape. The bars show the change in wave-length.

Control for Angle of Lean

There should be no surprise at the above findings as,

providing that the main bar response is a delayed copy of

the roll activity then excess values for the residuals

must produce the observed effect. The question is whether

155


the riders are using these pulses to control the machine

Or whether they are accidental inputs. No satisfactory

method of analysis has been discovered by the author for

examining

simulator

lean. The

continuous

has shown

this point conclusively. The runs on the

show that push inputs will produce changes in

regression analysis shows that angle makes no

addition to the bar movement and the simulation

that with only acceleration and velocity

controlling bar acceleration, any angle that accumulates

will remain in the form of a steady turn into the lean.

Since the riders all kept a more or less straight course

during their runs they must have been controlling for

angle in some way Or other and the extra pushes

represented by the excess residual peaks are the most

likely source of this control.

The angle traces show that all the runs have a tendency

for 3 or 4 seconds (100 points equals 3 secs) of a slow

drift of the mean lean angle followed by a fairly sharp

turn back towards the zero, executed within about 1

second. In order to get a clearer picture of how the

excess residuals relate to the movement of the bicycle the

location of the former were printed on the same time base

as the angle of lean curves (light line) from the upper

graphs in appendix 2, (b). These can be found in appendix

3, (c). The arrow direction shows the influence of the

excess push on the existing trace. That is, a residual

shown below the line in the previous graphs, such as that

at point 395 in run 33 (appendix 3, (b)), is shown as an

'up' arrow indicating that extra bar to the right (down)

gives a boost to the left (upwards) roll. Where an excess

residual push is attached to the X=O line it has been

omitted because of difficulty in seeing whether it is the

tail end of a wide pulse or a narrow one. Otherwise all

the recorded pushes are shown and no distinction has been

made between large and small ones. To establish whether

156


the excess residual pushes were in fact associated with

changes in lean angle the following analysis was

performed. The following criteria are taken as dividing

the roll angle response in the region of the pushes into

one of 5 categories.

Case 1. The direction of roll is the same as the

direction of the arrow.

Case 2. The slope changes direction in accordance

with the direction of the arrow.

Case 3. There is no movement either way.

Case 4. The slope is against the direction of the

arrow.

Case 5. The slope changes direction against the

direction of the arrow.

Three 'windows' of 300, 450 and 600 msecs width were

applied successively to each arrow so that the window

exposed the next angle values starting at the arrow

location. Each arrow was given three chances to obtain a

successful rating (case 1 or 2) by successively increasing

the width of the window. As soon as one of the two success

criteria was met the window size was taken as the score

for that arrow. If the arrow failed to meet one of the

successful cases then it was recorded as whichever of the

others was appropriate. The last two cases (4 & 5) were

combined as a single unsuccessful class. The results from

the 93 excessive residual points were as follows:

300 Msecs 66

450 Msecs

600 MSecs

Zero

15

5

o Contra (4 & 5) 7

Although the criteria for judging the slope movement

are somewhat subjective, a very large proportion fall into

the 450/300 mesecs acceptance category. One of the five

600 msec points (run 27 push 3) is right at the peak of an

157


appropriate reversal and only misses a 300 msecs category

because the rule starts the window at the point. At least

one of the contradictory points on closer examination can

be seen to be working in the successful bracket when

combined with the influences of neighbouring pushes. That

is, the effect on the acceleration movement does not

always lead to an observable movement in the angle. (This

was point 7 in run 33, already dealt with in detail

above. )

The above results suggest that the excess residual

pushes do lead to changes in the roll angle. It can also

be seen, especially in the first five runs, that the rapid

changes in angle already noted frequently have associated

residual arrows in appropriate locations. However it is

also true that there are some large angle changes with no

associated residual peaks. Run 25, point 240 provides one

example, run 27 point 200 another. Presumably there could

be a large peak just below the 1.96 threshold which got

its power from time of application rather than amplitude

and is therefore masked by the noise. The failure of an

arrow to appear on the first reversal of a long rapid

roll mo~ement such as at run 26 (265), rUn 27

(215) (360) (390) & run 29 (390) is not surprising as the

computer simulation shows that the roll/follow response to

a large externally imposed movement reduces the rate of

roll almost as quickly as the initiating movement. (figure

6.6 (a) Reversal at 2.5-3.0 secs). The pushes which follow

the initial reversal in the examples quoted would be

consistent with a rider putting in a push to counter the

shallow oscillating drift that follows the initial strong

reversal and force the bicycle back towards the upright.

Although it seems clear that the pushes identified by

the excess residual peaks are causing the bicycle to

change its roll angle it not so easy to establish what

feature might be triggering these inputs. The absolute

158


angle values for roll are unreliable as they are the

result of integrating the recorded velocities and the

constant term has been established only approximately.

The bar trace, which records actual angle not velocity,

has been used as a guide for 'zeroing' the angle data but

the exact distance of the various excursions from the zero

line are only approximate. It should also be borne in

mind that the angles involved here are small, less than 2

degrees. There are a number of examples of quite sharp

turns from apparently upright running (run 27,{320), run

33,{370)), but in general there are no sudden turns away

from the zero line when the lean angle is already

substantial. That is, any drift in lean is always curbed

not exaggerated. Thus the overall impression is that

somehow the control detects lean angle rather

approximately and, when this exceeds some threshold value,

pushes are used to bring the angle back towards the zero.

In the last three runs several alternate left/right

pushes have been introduced when the bicycle is running

upright, which make no overall change to the angle but

produce a comparatively large local wiggle. Feedback

control systems depend upon the changes in the primary

signal for their operation. When the signal gets too weak

it becomes swamped by noise and the control 'dithers'

about the zero waiting for something definite to appear.

Hunting to and fro either side of zero is one way of

improving the signal to noise ratio. Initially it was

supposed that the rider might be injecting short ballistic

pulses, timed to coincide with the zero crossings of the

roll acceleration, to give an increased response. However

a' more parsimonious explanation is that riders increase

the gain value to approach, or even temporarily exceed,

the 'just stable'

oscillations in

condition which results in large

the acceleration channel without

associated changes in the mean roll angle. When, however,

159


the bicycle is balanced near the upright there is little

actuating signal so the gain has nothing to mUltiply and a

high value will not produce a rapid change. It is

therefore possible that the left/right pushes observed

here serve the purpose of disturbing the upright balanced

position in order to improve the actuating signal.

Since the blindfolded riders had no direct information

about absolute angle they could only have recovered such

information either by some sort of neural integration of

the rolling and yawing acceleration or from sensory

changes at the contact points with the bike due to the

centrifugal forces during the turns. With the very small

angles involved the latter changes would be very small

indeed and the integrations would suffer from the same

sort of inaccuracy due to lack of the constant term as is

found in the data conversion. Both of these could account

for the lack of any clear regularity in the application of

pushes as r~vealed by the excess regression residuals.

Combined Intermittent and Continuous Control

A high correlation was found between the roll and bar

activity throughout all the runs, rising to a

places where the roll acceleration and velocity

accounted for over 95% of the movement in

acceleration (col.2, table 6.7) and was above

peak in

activity

the bar

SO% for

every total run (col. 2, table 5,3). Since the only

movement to the handle bar is through the rider's arm

movements it can be concluded that the basic control

system used by the riders applied the rates of angle

acceleration and velocity sensed in roll as rates of angle

acceleration to the handle bar after a delay that varied

about a mean of approximately 100 mesecs. The failure of

the angle term to maintain significance and constant sign

in a multiple regression over several seconds of run time

(col.S, table 6.6) indicated that angle was not

160

Bicycle Riding

continuously applied in

simulation showed that,

Chapter 6

the same way. A computer

with only acceleration and

velocity controlling the bar, the control failed to remove

angles that accumulated, thus a bicycle using such a

system would end up in a turn which would get tighter and

tighter depending on which way random disturbances

affected it. Th"e fact that the riders did remove turns

during the runs showed that angle must have been fed back

into the control in some form. When the points where

excess bar angle acceleration over that predicted by the

roll angle acceleration and velocity were plotted on the

same time base as the angle movement they were frequently

(87%) associated with an appropriate roll movement within

a half-wave length (mean 0.5 secs), but there were a

number of containing movements which did not have

accompanying excess residuals associated with them.

Simulated runs showed that pushes imposed over periods

greater than a half-wave length led to distortions in the

velocity curves which were not observed in the run graphs.

It was also noted that the maximum period for the excess

residual peaks was 300 msecs.

Overall it is considered that the evidence suggests the

riders were using a continuous delayed feedback control

which removed acceleration and velocity in a series of

'just stable' oscillations. As ang le accumulated some

threshold was exceeded and a push or series of pushes were

added to the continuous control to oppose the lean. The

small lean angles involved and the lack of direct

information about absolute angle led to a rather noisy

operation of the intermittent part of the system but the

general trend was a slow increase of lean during a series

of short wave oscillations and a short sharp change of

angle back towards the zero, which was then either checked

again with further pushes or allowed to settle down into

another slow change before the threshold for action was

161


again exceeded. The intermittent pushes were of a

ballistic nature, showing an exponential rise to a peak

and a similar decay. These pushes did not replace the

underlying movement but were added to it to produce a

composite wave form which means they must have been angle

independent, implying a muscle tension independent of

length. They were not timed in relation to the underlying

movement as they sometimes enhanced a wave and sometimes

inhibited it.

Variations in Lag and Gain

Change in lag, wave period and area was a feature of

all the runs. It is fairly certain that the phase lag and

gain would show small random changes about some mean even

if the control had no reason for altering them since

they are the consequence of neural operations which are

unlikely to be absolutely stable. Change in lag on its

own merely alters the potential stability of the system

and cannot be seen as an effective controlling

variable, and once the lag is fixed then the gain is also

fixed to give the best response without going into the

unstable condition. Thus it is argued that lag and gain

are reasonably stable values which remain fixed so that

the bar/roll follow control can operate effectively. It

can easily be seen that a push superimposed on an

otherwise perfectly regular bar/roll follow wave form will

cause large local disturbances to both the lag and

wave-period. Over the l2 runs there was an average of one

excess regression residual every 1.5 secs (12 runs of 400

points, ie 12 secs, 93 pushes) so it is evident that there

would be a good deal of disruption from this source and

since the pushes are not driven by the roll change the

initial movement would not be highly correlated with

that in the roll channel. As the roll follow responds to

the disruption the phase error is removed and the two wave

162


periods correlate more closely.

Thus it can be seen that it is a consequence of a

control where uncoordinated short pushes are superimposed

on continuous wave/follow activity that there will be

disruptions to the lag and wave periods which are

partly correlated between the roll and bar channels.

only

The

wave areas on the other hand are a reflection of the power

applied and will correlate more closely when the system is

maintaining a controlled path near to the upright. A

larger than normal bar push suddenly introduced does not

lead automatically to a large area for that wave as can be

clearly seen in run 33 (figure 6.9) around point 400,

since the extension of wavelength allows the amount of

power applied to balance. Referring back to table 5.4 in

chapter 5, it was noted that when the overall correlation

was high there was a more stable wave-period. This ties in

with what has been learned about the disruptive effect of

wavelength change on correlations and the conclusion is

that the wavelength disruption comes from uncorrelated

pushes added to the relatively stable underlying bar/roll

follow control, rather than changes in the lag or gain per

se.

Imitating Full Control on the Simulation

Figure 6.11 shows the simulated bicycle running under

fully automatic control with the speed and response values

trimmed to approximate those of the real runs. The bar

acceleration is a repeat of the roll acceleration and

velocity channels delayed 120 msecs. The gain has been set

at 220 to put the system near to the 'just stable'

condition to mimic the movement found in the real traces.

The intermittent rule applies a push of nominal value 16

applied over 300 msecs whenever the angle exceeds a

threshold of 1.6 degrees. To avoid applying a second push

before the first has had time to produce a change in the

163


lean angle, further pushes are locked out for one

half-wave period. The points at which the intermittent

control applies a push are shown by an arrow which relates

to the acceleration traces using the same convention as

before. The arrow points in the direction in which the

angle is driven. Figure 6.12 shows the first part of the

same run in a horizontal format similar to the one used

for the real run records so a comparison between the

general characteristics can be made more easily.

Secs

7

6

5

'" 3

2

~

Bike...£ 3 mph Gai n 220 La!) 120

R S R" S" (2) (5) (45) ( 142)

1.6-( )

\ .-(" ...

':-r'

~ ...

'-..J.. ) ...

Figure 6.11 Simulated automatic control. Basic control is repeat of roll acceleration & velocity at a delay of 120 msecs with the gain set to give a Ijust stable' response. When lean angle (R) exceeds 1.6 degs a 300 rnsecs push is added to the basic control to bring the lean back towards the vertical. Each push is shown by an arrow.

R' (5)

It can be seen that the intermittent threshold rule,

superimposed on the continuous roll/copy/delay control,

164


produces a trace that is very similar to those of the

actual runs. The local distortions to the roll

acceleration trace seen at 3.5, 5 and 7 secs, caused by

the addition of the triangular short push to the

underlying wave, may be compared with the distortions

shown in figure 6.10 and similar shapes in the run traces.

Bike.J: 3 mph Gain 220 Lag 120

.,....-7"'::., .. Angle

Velocity

Accln

1 2 3 4 5 sees

Figure 6.12 The initial 5 secs. of the run shown at 6.11 turned through 90 degrees to assist comparison with the record from the experimental bicycle under the same running conditions.

Nested Control Loops

Smiley et al. (1980) studied how the control technique

of naive car drivers altered with learning. When subjects

first started the task they tended to remove lateral

displacement errors by altering heading until the

displacement began to decrease and consequently

over-controlled. Since they also made corrections to

heading errors, independent of displacement errors, the

solution to the first problem led to a contra-response

from the second. In effect the two loops worked against

each other instead of in unison. As they gained

experience the subjects altered their technique so that

165


the two control loops were nested. A displacement error

was corrected by demanding an appropriate angle change in

the heading loop which continued to operate about this new

value until the displacement had reduced, at which point

the heading demand was returned to the original zero.

In the proposed control for the destabilized bicycle no

such nesting takes place. The underlying roll angle

acceleration and velocity loop continues to operate

autonomously. The push demand temporarily overpowers the

continuous control and imposes a roll errOr upon it. In

automatically removing the roll error the bicycle is

turned into this lean error which is the solution required

by the push. A similar performance is seen in bipedal

balance when runners sprint from starting blocks. The

initial instability is solved by accelerating the centre

of mass as fast as possible in the direction of lean. In

the bicycle the acceleration is provided by the turn

rather than the linear acceleration of the sprinter, but

it has the same characteristic in that it solves the

toppling problem by altering the acceleration of the

support point relative to the centre of mass.

Summary.

This chapter has explored the control technique used by

the subjects riding the destabilized bicycle in a straight

line, blindfold at very low speeds. In this condition a

normal bicycle has very little natural stability and the

experimental bicycle had none. The riders achieved basic

balance by repeating the roll acceleration and velocity as

steering angle accelerations. This allows absolute angle

to accumulate. When some lean/turn threshold was exceeded

the bicycle was forced back towards the upright with a

short pulse lasting less than half a wave period. The

next chapter considers how this control system might be

applied to the conditions found in normal bicycle riding

166


where the contribution of autostability becomes

significant.

167


7. CONTROL OF THE AUTOS TABLE BICYCLE

Normal Control

The previous two chapters examined in detail the

control used for riding a bicycle with all the

autostability removed. This chapter will deal with the

application of what has been learned to the problem of

controlling a normal bicycle. Three qualifications affect

the records taken from the normal bicycle. First the

limited length of the recording wire prevented any fast

runs. Second the records of bar movement contain

contributions from two sources, the riders' arm movements

and the autostability responses of the bicycle, and there

is no way of discriminating between these. Also, because

lateral body movements lead to autostability responses,

some of the controlling movements may come from this

source without there being any indication of this in the

records. Third, all the normal runs were done on the

Triumph bicycle before its conversion, consequently these

records differ from the ones already presented not only in

the presence of autostability but also in the extra weight

of the conversion. This, together with the remote steering

linkage, slightly altered the inertia and friction in the

steering assembly.

Low Speed Control with Autostability

A short summary of the autostability effects will be

given as a preparation for the discussion of normal

control. Due to the front-fork design three couples act

continuously on the front wheel. Whenever the frame is

rolling there is a precessing force trying to turn the

front wheel in the direction of the roll. Any increase in

the angle between the front wheel and the direction of its

168


local travel will produce a restraining couple, due to the

castor effect, which inhibits the movement. Whenever there

is an angle of lean the castor effect also gives a couple

trying to turn the wheel in the direction of lean. The

higher the speed the stronger the first two effects. The

greater the angle of lean the smaller the last two become,

because the geometry reduces the effective trail distance,

but this effect is not of major importance at normal

riding angles. These effects can only apply if the front

wheel assembly is quite free to turn under the influence

of the couples.

Autostability depends for its effect on speed. When the

speed falls below some limit there is insufficient

response

rider.

to prevent

The next

a fall without assistance from the

section discusses the differences

between ten runs on the normal bicycle with those already

discussed for the destabilized machine. The same subjects

provided five runs each and the conditions were exactly

the same in every respect as the destabilized runs except

that the bicycle was the Triumph 20 before conversion.

The traces of these runs are not presented but to a

casual inspection they are indistinguishable from the

destabilized runs reproduced at appendices 2, (b) and (c).

In order to compare the two sets of runs the values of the

matched waves, the extraction of which was described in

detail in the previous chapters, will be used.

Table 7.1, columns 1 and 2, shows a comparison between

nine characteristics of the two types of run. Column 3

shows the significance of a t-test between the two sets of

means. The justification for using the t-test is based on

the following argument. It is evident that during a run

the value of some variable such as 1ag or wave-length is

very definitely influenced by preceding values and

therefore violates the assumption of sampling independence

required for the t-test. However, if it is assumed that

169


the mean value for lag delay or wave-length or wave area

during a single run is a characteristic of the system

representing the combination of the bicycle and the rider

then it is reasonable to argue that there exists a

population of such mean scores which will be normally

distributed about some mean value over a large number of

similar runs. When some single value is changed, in this

case the change from the normal to the destabilized

bicycle, then this distribution either changes or remains

the same. Although the values for several successive runs

are still not truly random samples from this population

the t-test used has some validity in indicating whether

there are differences or not.

Variables Col. Norm. Destab Sig.

CCF roli/bar full run

Lag. Mean counted vals

Roll half-wave period

Bar half-wave period

Roll wave area

Bar wave area

Stand.dev. bar/roll

Corrln. roll/bar waves

Corrln. roll/bar areas

1 0.86

2 3.6

3 13

4 10

5 88

6 44

7 0.36

8 0.32

9 0.64

0.85 ns

3.7 ns

12 ns

11 ns

115 .01

103 .001

0.67 .001

0.56 ns

0.77 .001

Table 7.1 Comparison between the normal and destabilized runs for nine variables. Lags and wave-periods are in data-point intervals (30 msecs) and areas in nominal units. Values in rows 1 and 7- 8 are corrected to 2 places decimals, those in row 2 to 1 place decimals and in rows 3-6 to the nearest whole number. See text for details of t-test to which the last column refers.

Since the samples were not of the same size and

nothing was known of their variances a t-test of two

170


unrelated samples was used, (MICROTAB twosample). As will

be seen the correlations between the roll and bar angular

accelerations for the full run show no difference.

Although there were some differences between the two

individuals in the distribution of their lag values during

a run it can be seen that the combined mean values

over a run for either bicycle remain the same. Also the

mean half-wave period for the matched waves show no

significant differences. However the areas of the matched

waves in the destabilized system were significantly larger

than those for the normal bicycle, with a greater

difference in the bar than the roll.

The above results seem consistent with a combination of

autocontrol and human roll/follow control at low speed.

The autostability, which works almost instantly compared

with the rider's control action, reduces the roll angle

movements arising from both external disturbances

and the overcontrol due to the slower corrections of the

delayed human responses, but the speed is too slow for all

the movement to be removed. The wave period, which is a

consequence of the lag/gain ratio and the dynamic

properties of the system, remains the same in either case

but the areas which represent the power applied are less

than the roll areas because the automatic control is

limiting the roll departures earlier and therefore less

bar is needed tb contain them. The bar area is also

proportionally less in the normal bicycle output. Row 6

shows a cornparisbn between ratio of bar angle standard

deviations from the mean divided by roll angle standard

deviations. This is a measure of how much bar movement is

needed to contain the roll movement and confirms that the

autostable control requires less. At least two factors can

be identified which would promote such a difference. First

the greater the absolute lean angle the greater the

disturbing couple due to weight displacement so more bar

171


is needed to check a larger angle of lean, and, since the

autostability is checking the roll more quickly than

before, the angles will be smaller. However the angles of

lean in all cases were very small (see table 5.1) and it

is hard to see how a difference of 1 degree could cause

such a difference since the sine value hardly changes in

this regime. A second possibility is that the greater

inertia and less positive action in the modified front

fork design of the destabilized bicycle leads to greater

overcontrolling. The castor effect in the normal bicycle,

which works against all movements that try to push the

front wheel out of alignment with the direction of travel,

would also tend to damp out any overcontrolling due to

steering assembly inertia.

As expected row 7 shows that the correlations between

the roll and bar half-wave period are not significantly

different, although those of the normal bicycle are

slightly les~ correlat~d. However the areas do show a

difference although it is not clear why this is so. It

appears that for some reason when riding the normal

bicycle, although the subjects made proportionally less

bar movement per roll movement, more of this movement was

unrelated to associated movements in the roll. There is

the possibility that this was a learning effect since the

normal runs were done near the beginning of the

experimental period whereas the destabilized runs were

done after both riders had acquired considerable

experience of slow blindfold riding. That is, the extra

uncorr~lated bar movements could be noise due either to

unstable gain values or accidental or exploratory pushes.

In summary the comparison between runs on a normal

bicycle and runs on the destabilized machine at very low

speed shows few differences, which is consistent with the

idea that the autostability of the front forks is only

providing a marginal assistance to the human

172


roll-follow-at-a-delay control explored in the previous

two chapters.

Controlling the Normal Bicycle at Speed

The next question to be discussed is what control

movements the rider uses to direct an unmodified bicycle

at normal riding speeds. It has already been mentioned

that recordings of rider activity with a normal bicycle

are contaminated by the autocontrol. However with the

assistance of the simulation and some general observations

at fast riding speeds a fairly clear picture of the

necessary control system can be constructed.

General Observations on Fast Riding

The following experimental runs were made to obtain the

general response of a normal bicycle to some simple

control inputs at a speed where the autostability control

had enough power to remove any accidental roll errors. The

rider was a male weighing 178 Ibs in good current practice

riding a Carlton ten-speed sports tourer in good

condition.

a normal

Five runs were made

road surface

in each configuration on

down a hill whiCh was

sufficiently steep to maintain the speed without

pedalling. The speed did not need to be known accurately

but at the start of the each run the pedalling speed was

approximately 2 to 3 half-cycles of the pedals per second

in top gear (14/52 pedal/wheel ratio. 26 inch wheel).

This equated to between 17 and 23 mph at which speed there

was a high degree of autostability. Throughout the test

runs the rider made every effort to prevent any movement

between body and bicycle.

1. Inherent stability. The rider aimed to negotiate a

200 yard section of road without touching the handle bars

and without moving his body. The bicycle was extremely

stable with quite high forces in the steering due to the

173


autostability factors. On four out of the five runs the

bicycle ran straight and upright down the middle of the

road. On one run a single adjustment was made to heading.

2. Response to a disturbance. Once established in the

hands-off running configuration described in 1. above, the

rider pushed forward briefly with one finger on one handle

bar. The immediate response was a sharp lean towards the

side of the push. This was followed by a very rapid return

to upright running with one or two decaying oscillations

in roll either side of the vertical as the effect of the

disturbance damped out. A small change in direction

accompanied the correction.

3. Response to a steady push. From the hands-off

running configuration the rider applied a gentle push with

one finger to the end of one handle bar. The tip of the

finger was used so that only a push could be applied. The

push was held as constant as could be judged. The response

to this input was a rapid lean in the direction of the

push but this time there was no recovery. If the push was

applied rapidly there were a number of damping

oscillations about some mean angle of lean in the

direction of push; If the push was applied slowly the

angle gradually increased without oscillations. In both

cases the lean stabilized at an angle that depended on

the strength of the push and the bike went into a steady

turn in the direction of lean. Although the push was

maintained the handle bar reversed rapidly in the

direction of the lean under the autostability forces

during the start of the lean and during the turn the front

wheel was turned slightly in the direction of lean/turn.

4. Recovery from a turn. Once established in the turn

described in 3. above the rider rapidly removed the

pushing hand so that both hands were well clear of the

handle bar. The response was a rapid roll back to the

upright. This continued over the vertical so that there

174


was a fairly large excursion of lean to the opposite side.

Depending on the steepness of the original turn there were

two or three damping oscillations in roll either side of

the upright and the bicycle returned to straight steady

running.

5. Modified recovery. In this configuration the push in

the turn was removed smoothly and gradually rather than

suddenly. The response was a smooth gradual recovery to

upright running.

It was not possible to say for certain that there were

no associated body movements modifying the autostability

forces during these manoeuvres but the rider made every

effort to ensure that none was made and if there were any

unconscious movements they must have been very small. The

effects observed were exactly what would be expected from

an understanding of the autostability design of the

bicycle. Left to its own devices the autostability

resisted any tendency of the front wheel to leave the dead

ahead position. Any roll was removed by the gyroscopic

effect. Any lean was removed by the castor effect.

When the steering was displaced during upright

running with a short push a turn resulted in the direction

of the steering displacement, that is towards the side

opposite to the push. This turn led to a roll 'out of the

turn', that is towards the side of the push. This roll

caused the front wheel gyroscopic effect to produce a

precessing movement of the bar in the direction of fall.

This movement of the steering started a turn in the

opposite direction and thus balanced the fall.

When the bicycle was leaning over in the turn the

weight of the rider and the machine acted via the castor

effect to produce a couple with the trail distance,

turning the wheel further in the direction of lean. This

gave a greater centrifugal rolling effect than the

displaced weight couple and the bicycle was rolled back

175


towards the upright. These effects worked in unison to

remove any lean angle in a series of oscillations either

side of the upright.

When the autostability was modified by holding a steady

push to one side (out of the turn) the extra angle due to

the castor effect was opposed and the bicycle stabilized

in a turn. The gyroscopic force at this speed overpowered

the steering push and the resulting movement against the

push was an addition of the two couples. It should be

remembered however that at some steering/roll angle

combination depending on the design of the bicyle the

effective trail distance is reduced to zero and actually

becomes negative if the angle of lean increases any

further. (For example with the Carlton Corsair a steering

angle of 10 degs maintains a positive trail distance to

over 35 degrees of lean but an increase to 15 degs

steering reverses the trail effect at about 25 degs lean.)

Thus at very steep angles of lean the rider must modify

his technique in this respect. At some point the machine

becomes neutrally stable in roll and will keep turning

without any bar pressure. Beyond this angle it will become

increasingly unstable and will need into-the-turn pressure

to prevent its going out of control. This almost certainly

accounts for the 'uneasy feeling' encountered in fast

steep turns typically when negotiating a roundabout.

The above effects could only be seen in this clear form

when the speed was high. At low speed the autostability

forces were low compared with the disturbing effect of the

couple caused by the displacement of the centre of mass to

one side of the support point so that greater angles of

lean and rates of roll velocity were reached during the

corrections. Below some low speed the autostability forces

on their own were not enough to contain the disturbing

couple and had to be supplemented by movements from the

rider. It was noted that these movements tended to

176


include extra roll induced by upper body movements either

as well as or instead of additional arm movements. The

latter could not be subjectively experienced. The fact

that they must have existed was deduced from the fact that

when the hands were removed from the bar at low speed

control was lost.

The Effect of I?ushes on Control

It can be seen that the basic method of controlling the

normal bike for changes in direction is similar to that

seen in the destabilized bicycle. That is a push is added

to the continuous movement of the autostability control.

There is, however, an essential difference between the two

underlying systems. The destabilized control responded to

roll velocity and acceleration whereas the autostability

of the front forks in the normal bicycle will respond to

lean angle as well. When the speed is high, angle as

well as roll rate is removed and the bicycle will return

to upright running under autocontrol. A single on/off push

causes the destabilized system to take up a turn whereas

it merely causes a temporary disturbance in the normal

bike which returns to upright running as soon as the push

is removed. In order to keep the bicycle turning in the

latter case the push has to be maintained.

This difference is illustrated on the simulated model.

Figure 7.1 shows the effect of a single on/off push on

each in turn. The time of application of the disturbing

push is the same in both cases but the force has been

adjusted to give exactly the same initial excursion of the

handle bar acceleration (S' '). Because the castor effect

produces a strong damping effect on any steering movement

out of true the force needed to produce a similar effect

on the bar is higher by a factor of 5. In the upper

diagram the simulation responds in the same way as the

bicycle in the high speed tests in that the initial

177


disturbance is damped out after two decreasing

oscillations and upright running is rapidly resumed.

Secs

a

2

J.

Secs

BIKE..£ R

8 mph

( 2)

BIKE..£ 8 R

( 2)

S ( 2)

mph S

( 2)

(

Norma 1 bicy c le R·· S··

(50) (70)

Gain 220 R"

(50)

Lag 10 s"

(70)

R' (5)

R' (5)

Figure 7.1 The effect of a single on/off push on the autocontrol. (upper graph) and destabilized system (lower graph). The push is applied over the same time interval with the strength trimmed to give the same initial response from the steering acceleration (S") .

In the lower diagram the roll acceleration (R") is

damped out with the trace showing a mean of zero. The

velocity (R') is initially displaced to the left by the

push but returns to a mean of zero after about 3 seconds.

178


The angle

and the

incurred during this operation is not removed

destabilized bicycle continues to lean and

therefore turn in the direction of the disturbance (R).

The scale in the roll channel has been left large

deliberately so that a direct comparison may be made

between the two figures. The gain and lag in the

destabilized control has been chosen to give a lightly

damped converging oscillation.

Secs

3

J.

8IKE.J:

388

R (5)

12 mph S

(2)

Normal bicllcle R"

(50)

~ . ..... -

s" (75)

R' (10)

Figure 7.2 Simulation of push control of the autostable bicycle at 12 mph. A single 'on' push turning the bar to the right (right peak in channel S'I at 0.3 secs) gives a smooth roll to the left. The autostability forces immediately respond and check the lean at 7.5 degrees giving a steady turn left until the push is removed (left peak in S" at 2.25 secs) when it returns to upright running without further attention.

179


Controlling the Normal Bicycle in a Turn

It was seen in the high speed tests that a push held on

the bar led to a balanced turn in the direction of push at

a rate that depended on the strength of the push. It was

also seen that gently removing the push once in the turn

led to a smooth recovery to the upright. Figure 7.2 shows

this operation simulated on the model at 12 mph. The

push to the right causes an excursion of the bar in that

direction (S) . The autostability forces rapidly oppose this

and under the combined effect the bar moves to the left to

follow and contain the fall by 7.5 degs. The result is a

steady lean and therefore turn to the left. When the push

force is removed at just over 2 secs (note the sudden

left excursion in the steering acceleration channel S")

the unrestrained castor effect moves the bar further left

causing the centrifugal couple to dominate the falling

couple and the bicycle returns to the upright with one

gentle oscillation. Thus the technique for turning a

bicycle at a speed where the autostability is high is to

apply a gentle push in the desired direction of turn,

maintain the push until it is time to recover and then

remove it upon which the bicycle automatically resumes

upright running.

The faster the speed, and therefore the higher the

autostability forces,

strength of push.

the smoother the response to a given

When the speed falls and the

autostability forces begin to reduce, the push must also

be reduced to keep the control smooth. Steep turns at low

speeds are therefore likely to be more oscillatory.

Unfortunately no systematic recordings were made of

manoeuvres but some rather casual recordings were made

early on of the entry to and recovery from a turn with the

normal bicycle at about 7 mph. Unfortunately two of the

subjects were unable to carry out this manoeuvre without

going out of control and their productions are of little

180


use except as an interesting example of overcontrolling.

However one subject produced a good trace of a smooth

entry to and recovery from a turn and this is shown in

figure 7.3.

Run No. 10 Roll and Bar (dark lines)

ANGLE

VELOCITY

ACCLN

I I I I I I I I I I I I I I I I I I

data points 100

I I I

200

I I I I I I I I

3

Figure 7.3 Showing the angle, velocity & acceleration for roll and bar (darker lines) for a 360 degree tUrn (Run 10) on the unmodified bicycle with a sighted rider. See text for details.

181


Single Recording of a Successful Turn

This run was made on the normal Triumph 20 bicycle

before modification. The recording was made at an early

stage of the experiments when the recorder was using four

channels instead of two which gives an interval of 56

msecs between recorded points. The rider was the same

subject who produced the high speed observations and for

this run he was not blindfolded. The instructions for the

run were as follows. The rider accelerated to a

comfortable riding speed on a course which took him back

along the wire and across the front of the recording

station. The recorder was started as soon as run speed was

achieved. At some point approximately opposite the

recording station the experimenter called 'now' and the

subject initiated a turn to the right as quickly and as

steeply as possible consistent with smooth control. The

turn was continued for 360 degrees holding as steady an

angle of lean as possible at which point a smooth

recovery was made. The run was terminated once straight

running had been resumed. The actual mean angles during the

turn were 9 degrees of lean and 5 degrees of bar. The

radius of the turn was measured as approximately 15 ft so

the speed can be calculated from the equation:-

Force = Mass x Speed A 2 / Radius

where the force is that needed to produce a couple to

balance the weight couple at 9 degrees lean with a weight

of 200 lbs and a lever arm of 3 feet. This gives a speed

of 6 mph. This also cross checks with the time for the

turn recovered from the graph of the run. A 15 ft radius

turn has a diameter of 94 ft which takes 11 secs at 6 mph.

There are 200 points of 56 msecs each between the

initiating spike and the recovery, ie 11.2 secs.

It is not possible to discriminate between arm induced

182


bar movements and secondary effects due to body lean in

the traces from the normal bicycle. Whichever method is

used, and there is a likelihood that a combination of both

methods is the normal technique, the only way a rider can

initiate a large roll rate is by moving the bar to give a

turn in the opposite direction to the desired roll. Figure

7.3 clearly shows this initiating movement of the bar at

the start of the turn in all three graphs and the

corresponding rapid increase in roll angle. For about 80

points after the initiation there is some 1 hertz

oscillation which damps out. Between points 160 and 210

the record shows very little movement in the rate traces

which is due to the inability of the recording system to

capture the reduced movement when the bicycle is under

autocontrol alone. The extra filtering in the jerk trace

removes all the bar movement and most of the roll between

the initiating spike and the recovery so this channel was

not included in the figure. After the recovery there is a

resumption of the 1 hertz oscillation. This record shows

that the rider was able to hold a steady push on the bar

between point 160 and 210 which just balanced out the

castor effect and left the bicycle turning steadily under

the gyroscopic effect.

Table 7.2 shows the statistics for this run. Because

of the difference in channel interval, results have been

converted to milliseconds so that a direct comparison can

be made with the results for the previous runs. These

have been taken from tables 5.3, 5.6 & 6.3 and show only

the results for runs 25 to 30, since these were the

contributions by the same rider. The full run correlation

for the roll and bar acceleration at 0.87 is comparable to

that for the destabilised bicycle at 0.84. This was

achieved at a lag of 112 msecs as opposed to 115 msecs on

the destabilized system. There are only about a dozen

distinct waves in this run and these were measured by eye.

183


Consequently the measurement of the matched waves is

rather approximate. However the mean lag measured at 117

msecs compares with a mean lag for this rider in the

destabilized runs of 122 msecs. The half-wave periods in

the oscillatory parts of the run are somewhat longer but

show the same sort of relationship to each other as

indicated in the bar/roll ratios. No attempt has been

made to make a meaningful conversion of the wave areas

between the two systems so these have been omitted.

The regressions for the first 170 points predicting

bar from acceleration, velocity and angle show a similar

pattern to those for the destabilized runs. The

acceleration and velocity account for 81.5% of the bar

movement which rises to 85.7% when the angle term is

included but this is unreliable as the latter does not

give a significant contribution. The significance of the

velocity and acceleration terms remain above the p<. 01

level in both regressions.

Variable Run 10 Destab

CCF roll/bar whole run. 0.87 0.84

Lag for best correlation. (msecs) 112 115

Lag, mean at zero-crossings. (msecs) 117 122

Roll half~wave period. (msecs) 587 416

Bar half-wave period. (msecs) 424 367

Ratio of bar/roll half-wave. 0.72 0.88

Table 7.2 Comparison between a medium speed manoeuvre on a normal bicycle (Run 10, fig. 7.3) and the mean of 6 straight slow runs on the destabilized bicycle (runs 25-30, rider A) using B variables. Lag and wave-periods have been converted to msecs. Correlations and ratios are corrected to 2 places of decimals. Msecs are corrected to the nearest whole number.

184


The overall picture shows that at this speed the

autostability is not powerful enough to cope with the high

rate of roll-in imposed by the initial push and during the

entry to the turn the rider is supplementing this with the

sort of control seen in the destabilized runs giving the 1

hertz wave in these portions. For the second half of the

turn the rider achieves a stable solution and the bicycle

turns under autostability control alone although the

recording is too coarse to pick up the much reduced

movements. The release of the holding-in push can be seen

in the angle bar trace between 215 and 240 and this is

seen as a suppression of the appropriate response to the

rising roll at 230 in the acceleration trace. Despite

this fairly gradual initiation the autostability cannot

deal satisfactorily with the check at the upright and the

rider again brings in

and the end of the

supplementary control between here

record. The evidence from the

simulation runs and the high speed runs indicates that had

the speed been higher the autostability could have dealt

with this problem on its own. Similarly had the rider in

this run rolled in and out more gently then the

indications are that the same would have applied even at

this lower speed.

It must also be borne in mind that during this run the

rider could see and therefore had immediate information

about lean angle available. However, the oscillations

just after entry and particularly after recovery suggest

that this did not lead to a mOre sophisticated application

of angle, but that the rider was still using the technique

observed in both the destabilized and normal very slow

runs. That is, he was using short pushes to obtain changes

in lean angle.

The rider would also have been able to enhance the

autostability effect by making rolling movements of the

upper body which would not be detected by the recording

185


system. On the recovery, for example, he could have

allowed the frame to rotate over the upright while keeping

his upper body in the vertical (a local upper body roll to

the right) which would give both a gyroscopic precession

and a castor effect to the left, providing a force opposed

to the combined mass movement. The recorder, being fitted

to the frame, would pick up this movement as a roll past

the vertical whereas to an observer it might seem as

though the rider had stopped in the vertical. That is, the

recording device only shows the movement of the combined

mass when there is no relative body/machine movement. Such

body movements do seem to be made at intermediate speeds

and although the precessional response of the front wheel

is very quick the body movements themselves

slow due to the inertias involved.

Imitating the Turn on the Simulation

are fairly

The above run can only be imitated on the model

approximately because of the low speed and high roll-in

rate. The model cannot be seen as an exact representation

in detail of the real events so its performance at an

equivalent speed is not necessarily exactly the same, nor

is the added ingredient of body movement modelled. If a

push strong enough to give the initial roll-in rate of 10

degs per second is applied and the autostability is left

to its own devices the result is a large oscillation with

a mean of about 7 degrees (R in Figure 7.4, (a». Similarly

if this push is removed rapidly at the end of the turn

then the initial rate of roll-out is the same as the real

trace but there are large oscillations about the zero lean

position. However by a little juggling of the input a fair

representation can be achieved.

The difference needed on the entry is to check the roll

angle at the desired angle of lean without reducing the

high rate of entry. This must be achieved by removing the

186


pressure that is driving the roll at some critical point.

BIKE...c 6 mph S

(5) Secs R

258

4

1

Secs

I

(5)

BIKE...c 6 R

(5)

mph S

(5)

Normal Bicycle R·· S··

(70) (142)

Normal Bicycle R" S"

(100) (294)

R' (20)

R' (20)

Figure 7.4 Imitating the real trace of a turn and recovery. If a push strong enough to give the same roll-rate as th~ real trace is applied and held (upper figure (a» the resulting turn is oscillatory. When the technique is slightly modified (see text) the characteristic is nearer the performance of the real bicycle and rider. (Lower figure (b».

The two outputs can be made to match by reducing the

initial push back to zero in the standard push period

immediately following the rise. Thus the input takes the

187


form of a pulse, rising to a maximum and falling back to

zero at the same rate. This allows the bar to move further

in response to the autostability couple, thus checking the

fall earlier. If the tension were left at zero then there

would be a strong roll back towards the upright after the

fall was checked, so it is obvious that tension must be

reapplied to keep the machine in the turn.Reapplying the

original push here produced too strong an effect but by

experiment a push of half the original value was found to

check the fall mOre Or less dead beat as in the original.

The recovery can be imitated in the same way. Since it

can be seen from the unmodified control used for figure

7.4, (a) that merely removing the bar push leads to over

control, then some extra step must be taken to prevent

this happening. Removing the pressure at a very low rate,

over several seconds, smoothly returns the lean angle to

zero without over-control but this is not what the rider

in this run has done. A strong recovery is initiated when

the pressure holding the bike in the turn is released.

Since this does not lead to a large overrun then pressure

must have been reapplied at some subsequent point to

damp this out. A range of matched amplitudes and timings

may be used to produce very similar traces in the computer

output. The trace shown was achieved by setting the

pressure to zero within the standard time increment thus

starting a strong recovery. Half the original value held

during the turn is reapplied after the recovery has got

under way thus facilitating the autocontrol response to

the rising roll which is checked as the bike reaches the

upright rather than going beyond it. The pressure can be

completely removed anywhere in the region of zero lean

without making much difference to the behaviour. Once

again it is emphasized that the above modifications could

be equally well achieved by upper body movements which

recruit extra autostability responses, but since the

188


simulation does not include body movements they must be

shown in terms of extra arm forces.

Angle

.- -~. ~---..---, '-----,., '--... ------_ .... ,--

Velocity

.- -.--"

Accln

1 2 3 4 5 Secs

Figure 7.5 The simulated run shown in figure 7.4 (b) transposed to the same axes as the actual run shown in figure 7.3 to assist a direct comparison of the characteristics.

The output giving rise to the traces in figure 7.4, (b)

has been transferred to horizontal axes in figure 7.5 to

make a visual comparison between the computer simulation

and the original run traces in figure 7.3 easier. Since

the modifying pushes described above are fed in from the

keyboard, the run in 7.5, although the same in principle

as that in 7.4, (b), is not exactly the same in detail.

It can be seen that although the details of the

simulated run and the real run are different the general

characteristics are very much the same. It is the

imbalance between the rate of roll-in and the riding speed

that has caused the difficulty here since figure 7.2 shows

that at a higher speed just a straightforward push and

release achieves almost exactly the same characteristic as

189


the actual run.It is interesting to note that two other

less experienced riders who attempted to make a similar

manoeuvre were unable to do so, both going out of control

after the entry point. They initiated a strong roll-in on

the 'now' call but were unable to control the check at the

required lean angle. Consequently, although the difference

between the simulation and the real trace may be due to

the model failing to reproduce the correct response at

this low speed, it is equally possible that forcing the

bicycle to perform smoothly in this way at low a speed

requires a higher degree of skill than that possessed by

the two riders who failed and that the successful run was

achieved by the more experienced rider supplementing the

basic push control with either more complex arm movements

or appropriate body movements.

Directional Control of the Normal Bicycle

Thus it can be seen that control of the machine at

normal speeds is achieved in the following manner. The

design automatically ensures that roll disturbances are

damped out and the bicycle will return to upright running

ftom low angles of lean. Allowing for a certain amount of

low frequency oscillation, lean and turn are always

equated. An angle independent tension on the handle bar,

added to the autocontrol couples, will cause the bicycle

to roll in the direction of push and then to turn in that

direction, despite the rather confusing fact that the push

appears to be in opposition to the required turn.

Releasing the push causes the bike to recover to the

upright. It is now evident that the rider's contribution

is exactly the opposite to that used for a car or a

tricycle. A push with the right hand in fact turns the

handle-bar to the left. The reason the bar then turns back

into the fall is due to the autocontrol couple not the

rider's push which is actually opposing it. If the rider

190


were to ignore this and turn the bar in the desired

direction of turn the result would be a violent

uncontrolled fallout of the turn. The informal survey,

mentioned in chapter 3, suggests that riders generally

believe that they themselves turn the handle bar into the

initial roll and are unaware that in fact they are holding

an angle independent push in the opposite direction

throughout the turn. In reality reversing the push forces

a very rapid recovery from the turn.

Mixing the Two Systems.

So far two somewhat different directional control

systems have been proposed. Both systems achieve a turn

by applying a push which turns the handle bar initially in

the opposite direction to the desired turn. When the

speed is Iowa short on/off push produces a fairly sharp

roll fOllowed by an oscillatory turn and when the speed is

high such a push will only produce a wObble so the push

must be maintained to achieve a turn. The question arises

how does the rider know which method to employ and do they

interfere ~ith each other? Because the bicycle

autostability has, by comparison with the human control,

virtually no delay before responding and because the

castor effect needs a high force to overcome its damping

effect, the forces associated with the former anticipate

in time and completely dominate in degree those of the

latter. The faster the speed the greater this discrepancy

as the castor da~ping effect keeps rising with increased

speed whereas the bar forces in the undamped manual

control must be reduced to compensate for the increasing

force-per-wheel-angle response.

In practice the general sensitivity to response rate of

human control mentioned in the previous paragraph is

sufficient to allow a smooth change over of control as the

speed drops below autostability levels. When there is

191


good autostability then the small forces involved in the

manual system fail to make any appreciable contribution

but because autostability is working this contribution is

in any case redundant. As the speed falls the

autostability forces reduce until, at the point where they

begin to fail to get a grip on the errors the weaker

manual forces become significant and either supplement or

take over the task.

Individual Differences.

This study was primarily intended to discover the

general technique of bicycle riding. The ski 11 is so

common and yet so constrained that it was one of the

initial hypotheses that there would be few large

individual differences in the characteristic of

responses. It was also realized that only when the details

of the control being used was known would it be possible

to design experiments which highlighted the differences

between different riders. The study has not proceeded

beyond the first stage and all the data comes from only

two riders. These data, representing some 7 mins of

control, are adequate for establishing the general

principles involved but do not form a basis for a proper

comparison between individuals' performance. However, some

comparisons between these two riders are tentatively

presented and the MICROTAB twosample t-test for two

unrelated samples with different variance is used to test

the differences following the same logic as before. That

is a mean of such a value as lag or wave period for a run

is regarded as one of a population of such values for this

individual on this machine doing this task. Table 7.3

shows a comparison of the same values used for the

normal/destabilized comparisons. The data are those from

five normal runs and six destabilized runs for each rider.

192

Bicycle Riding

Variable A M

Lag measured at zero-cross 4.2 3.1

Roll half-wave period 14 11

Bar half-wave period 12 10

Bar wave area 112 95

Roll wave area 87 66

CCF whole run 0.85 0.86

Corrln. bar/roll wave 0.41 0.48

Corrln. bar/roll area 0.67 0.74

SD ratio bar/roll 0.52 0.53

Table 7.3 Comparison between the two riders using nine variables. Lags and wave-periods data-point intervals (30 msecs), wave areas in units. Correlations and ratios corrected to 2

Chapter 7

Sig.P<

.001

.001

.001

ns

ns

ns

ns

ns

ns

(A & M) are in

nominal decimal

places, lags to 1 decimal place and the other values to the nearest whole number.

Row 1 shows that there was quite a difference between

the lag values over these runs and the t-test shows this

to be highly significant. The histograms in appendix 2, (c)

show that there is a considerable difference in the

distributions, rider A having a wider spread of values

about the mean. Rows 2 and 3 show that rider A had a

significantly longer wave period that rider M. The

simulated runs showed that with shorter lag a higher gain

could be used for the same stability and that higher gain

gave a shorter wave-length. It can be seen from the angle

traces in appendix 2, (b) that both riders used a

combination of lag and gain that put the system somewhere

near the 'just stable' condition, thus, assuming that

lag is a basic value for the rider, the wave-period should

show a difference in the same direction. The t tests show

193


that the differences in mean roll and bar areas were not

significant, which implies that despite differences in lag

and gain the two riders moved the bicycle either side of

the mean path about the same amount and used approximately

the same amount of power to do so.

The whole-run correlations between roll and bar

acceleration were almost exactly the same (row 6) as were

the correlations between the matched roll and bar waves

both for period length and area Or power. The ratio

of bar to roll standard deviation, the measure of how much

bar was needed to achieve control (row 9) are almost

identical. These last results are an indication that the

system is so unstable that it leaves very little room for

alternative solutions to these relationships.

The overall picture is one in which both riders

produced very similar performances on either machine.

There are some indications that the lag value is different

for each rider and since the lag value for rider A was the

same when riding sighted at higher speed during the turn

manoeuvre it looks as though this might be an individual

characteristic. No rider could have a mean lag much in

excess of 150 msecs and still generate enough power to

control a bicycle in normal riding without going into the

unstable diverging oscillatory regime. There must also be

some lower limit for lag due to the time taken for the

sensory mechanism to react to changes and transmit these

to the operating muscles. There is not a great deal of

leeway in this value and it would be expected that

measures taken for a large number of riders would show a

distribution of differences with a mean of somewhere about

100 msecs and accompanying adjustments of gain (and

consequently wave period) to keep the system somewhere

near the 'just stable' condition. Presumably this latter

feature is a method of keeping a good signal to noise

ratio for the control response to work on.

194


Summary of Bicycle Control

Because the bicycle is so unstable there is little

freedom of choice when postulating control systems. When

the autostability of the normal bicycle is removed the

rider supplies a very similar, though less efficient,

control. The acceleration and velocity movement in roll

detected by the rider are applied continuously via a

suitable gain factor to the muscle tension in the

controlling arms. Because the human is appreciably slower

than the autostability to apply this correction there is a

delay of about 100 msecs between the roll curve and the

bar curve. This produces a torque in the steering head

which damps out the roll movement in a series of

oscillations, taking the form of a 1 hertz wave. This

torque is supplemented by short pulses of additional

tension which produce a temporary shift in the balance of

the left and right velocity oscillations giving an initial

sharp change in lean angle followed by a series of damping

oscillations giving a slower 0.2 hertz wave superimposed

on the shorter wave.

The human roll stability does not conflict with the

mechanical autostability control because it is much slower

and uses much lower push values. When autostability is

present it dominates the human contribution but gives way

to it smoothly when at very low speed it fails to produce

sufficient controlling effect.

In normal operation riders may be observed to roll the

upper body out of turns at low speed presumably in order

to increase the autostability effect. However, since none

of the riders had any difficulty riding the destabilized

machine without extra training it appears that beginners

learn the roll-follow technique to start with and do not

forget it even though it is not often needed for normal

riding. This seems reasonable since children's first

195


bicycles tend to have poor autostability and learning is

obviously done at a very slow speed.

Full Navigational Control

Once the system is able to control the angle of lean in

this way it has the necessary power to implement

navigational instructions. The 'roll-follow at a delay'

control, although slower and more oscillatory, is in

essence the same as the autostability control. In both

systems the roll acceleration and velocity are damped out

and the absolute angle is controlled by integrating a

pulse input of angular acceleration with the other inputs

to the steering head. When higher order mental operations

require a turn in one direction or another this must be

converted into the instruction 'push left to go left' or

vice versa. Presumably, at some higher level of

organization, the rider would be aware whether the speed

was high or low and would modify the instruction

accordingly. Selecting 'high speed' in error would lead to

a severe wobble and possibly loss of control whereas

mistakenly selecting 'low speed' would merely lead to an

absence of response.

Of course the story does not end there. It was seen

in chapter 4 that as the angles of lean and steering

increase so the trail distance reduces until at some angle

which depends on the geometry of the bicycle it actually

reverses. Steep turns, particularly at low speeds where

the steering angle will be large, approach this reversal

point and as they do so less and less push will be

required to sustain the turn. If the critical point is

passed then the castor will work in reverse and the rider

will have to provide a push in the opposite direction to

prevent an unrestrained increase in lean. The rather

uncertain feeling

doubt due to the

engendered by very steep turns

decreasing castor stability.

196

is no

It is


evident from Jones' (1970) experience with the

exaggeratedly reversed castor bicycle, URB IV, that

providing such a push is within the scope of normal riding

skills, although he reported that it felt 'very dodgy'.

This is understandable for, unlike the destabilized

bicycle which produced no mechanical torque on the

steering, a reversed castor effect is actually trying to

turn it the wrong way so the customary gain setting would

be much too weak to oppose it. Jones' underlying control

worked in the correct sense but would have needed

considerable trimming to deal with the new problem.

Despite the discomfort produced by the reversal of the

trail distance the general control technique remains 'push

on the side towards which you want to roll'. The

consequences of pushing the wrong way are so rapid,

dramatic and final that it may be seen that in general the

problem of control is not so much finding which way to

push to get the desired roll but adjusting the gain and

keeping the push angle-independent to prevent overcontrol.

197


8. BIOLOGICAL CORRELATES OF THE CONTROL SYSTEM

The Requirements

This chapter considers what structures might support

the proposed control system. No claims are made about

exclusive neural pathways, simply that the requirements of

the model do not contradict existing physiological

knowledge. The model requires two things. First that

accelerations in roll lead to matched accelerations in bar

movement within a period of approximately 100 msecs.

Second it requires that an angle independent tension can

be applied to the handle bar for the duration of an

intended turn.

Lee (1975) argues convincingly that the most sensitive

and efficient proprioceptive organ for sensing roll

movement is the visual system. He showed that it is

superior to the vestibular system and in circumstances of

conflict will dominate it. He also demonstrated that it

can exercise direct control of the postural muscles

without the subject being aware that any change is taking

place. As soon as it was discovered that if a person could

ride a bicycle sighted they could also ride it blindfolded

without any retraining it was decided to run the

experiments in the latter mode for two major reasons.

First the riders having no obvious path to adhere to would

be more likely to obey the instruction not to remove any

turns which occurred and second the performance without

vision was likely to be less accurate so there would be

more movement in the traces which was important since the

sample rate was rather marginal. The mechanoreceptors in

the muscles, joints and skin are also used for small

postural adjustments but as Lee points out their

efficiency varies with the posture and the nature of the

surface of contact. None of these sensors are appropriate

to the basic bicycle balance task because pure roll does

198


not produce any change at rider bicycle contact points.

However during a balanced turn there will be a slight

increase in pressure similar to the sensations encountered

when a lift stops. This is a possible source of

information in judging the threshold at which to initiate

a recovery but the lift analogy should warn us that the

system has a rather high threshold in this respect since

very smooth lifts succeed in stopping without transmitting

any sensation. Thus it can be seen that for these

experiments the roll detection requirement will be

satisfied if it can be shown that an output from the

vestibular system, proportional to short-period roll

accelerations, is fed via a reasonably short neural

pathway to the gamma and alpha motoneurones of the arm

muscles in such a way as to create in them a proportional

tension without interference from antagonistic muscles and

synergistic stretch reflexes.

The Vestibular System

The vestibular apparatus is a mechanism shared by many

species. Its structure and operation have been

extensively explored and the details are described in

introductory text books. (e.g. Davson & Segal, 1978). In

order to give a quick response to out-of-balance movements

the neural connections take a characteristically short

path to the relevant motor structures. The organs are

situated in the inner ear, one on either side of the head.

Each has three semicircular canals which respond to the

relative movements between them and the fluid they

contain. These lie in three mutually orthogonal planes so

that any pair can be excited maximally by a rotation of

the head about one of the three axes. The responses are

fed via the vestibular neurones to the vestibular nuclei

where they give an integrated output defining the

movement of the head.

199

Bicycle Riding

cortex

reticular formation

Chapter 8

semicircular canal

vestibular nuclei

to spinal motor neurones

Figure 8.1 Pathways from the vestibular system to the limb muscles. Output can go either direct or via the reticular formation which is open to modification from the cortex. (Adapted from Davson & Segal, 1978)

Figure 8.1 shows a formal representation of the way in

which information about the internal arrangement of the

parts of the body is integrated with information from the

vestibular system via the reticular formation. This is a

region of the brain stem exerting a powerful influence on

the skeletal musculature and consequently an important

control-centre for the organization of movement.

There have been a number of experiments addressing the

question of direct pathways from the vestibular system to

motor control neurons. For example Eldred (1953) showed

that a powerful influence was exerted on gamma fusimotor

neurons by the vestibular system and this was confirmed in

subsequent studies by Grillner et al. (1969), while Lund

and Pompeiano (1968) showed that the extrafusal alpha

motoneurones also received monosynaptic activation from

the same regions. Lund and pompeiano concluded that only

extensor motor neurones were activated but Grillner et al.

considered that those of the flexors were also activated

via the reticular formation which has close connections

with the vestibular output.

200

Bicycle Riding

Deiter's nucleus

extensor

Chapter 8

Medi I'll 1 ongi tudi nl'll

fasciculus

Figure 8.2 Schematic representation of descending monosynaptic effects via fast conducting fibres from Deiter l s nucleus and the medial longitudinal fasciculus on the alpha and static gamma neurones to flexors and extensors acting at the knee-joint. All synapses are excitatory. (Adapted from Grillner I 1961))

They proposed the connections illustrated in figure 8.2

for the knee joint showing influences of both intra and

extrafusal efferents from Deiters nucleus, which is a

vestibular nucleus, and the medial longitudinal

fasciculus, which is the main pathway taken by the

reticulospinal fibres to the motor neurones.

The vestibular mechanism has two sorts of transducer,

the otolith organ in the utricle and saccule, and the

ampulla in the semicircular canals. Figure 8.3 shows the

general arrangement of these structures in the inner ear.

Detailed research into the output performance of the

otoli th organ has not been as extens i ve as for the

ampulla. The exact role of the saccule is uncertain.

Ablation seems to have no adverse effect on balance though

there is some evidence that visual acquisition may be

201


affected. The utricle responds principally to changes in

the rolling and pitching plane.

the semi-circular canals

ampulla posterior

ampulla anterior

ampulla lateralis

vestibular --~ ____ ~---------- nerves

F i gu re 8 . 3 The semicircular canals the inner eat.

general arrangement of the and the sensory transducers in

The general form of the discharge rate is a

linear function of the effective force acting upon the

organ (Fernandez et al 1972). It should be borne in mind

that the way in which the total system integrates all the

outputs from the various transducers at the vestibular

nuclei during head and body movements is not known in

detail. However, it seems fairly certain that the main

function of the otolith organ in balance is to give a

response to the statiC relationship between the head and

the pull of gravity.

The operation of the ampulla, which responds to the

relative movement between the semicircular canals and the

endolymph they contain,

deal of research.

observations of the

has been the subject of a good

Steinhausen, following direct

cupular of the carp in 1931,

formulated the proposition that the movement under

acceleration acted as a heavily damped torsion pendulum.

(Summary in Ha11pike and Hood, 1953) . Unfortunately such a

202


model predicts that the output will fall to zero for the

very short-period excitation which is the more normal

type of stimulus encountered in everyday movements.

Despite this the model was adhered to for many

leading to a dearth of experiments exploring

particular range of values. Some light, however, is

on this subject by Fernandez and Goldberg (1971).

years

this

shed

They

studied the output of selected neurons associated with the

semicircular canals of the squirrel monkey when the animal

was subjected to controlled rotations in a cage-like

apparatus. When sine-wave inputs controlled the movement

of the monkey's carrier it was seen that the response no

longer followed the predictions of the damped torsion

pendulum model. The information obtained from these

experiments was used to modify the equations, by altering

the time constants, until the predictions followed the

observed output. Using the new values they predicted the

responses to three rising half sinewave accelerations in

the range of interest. These predictions are shown in

figure 8.4. The upper graph shows the predicted response

to the three stimuli. The lower graph shows the change of

velocity for these on the same time scale to emphasise

that the vestibular system discriminates between them with

different spike rates even though they all peak at the

same maximum velocity. Although this is a prediction, not

an experimental result, it is a reasonable extension of

the findings of the paper and gives a clear indication

that the vestibular system is capable of producing a

response that is proportional to the rate of angular

acceleration. This is the sort of performance needed to

drive the projected bicycle control model.

203


Response

; ('.!AihL::~_ ......... (_cana

1 output)

, J\ Normalized response 0

(spikes/sec) -1

-2

-3

Angular velocity 0 (deg/sec)

.. ;:; ... : . .. '.: :. .:. :.: .:. _.:::-.: :,' .: :.: .: . . : :', :',

\,8 htz ':l:l:

::: ..... ::. 8 htz

4 htz 2 htz

Stimulus (change of position)

Figure 8.4 Showing how the response of the semicircular canal to short period rotations discriminates between different rates of acceleration (spike response, upper graph) even though the final angular velocity is the same in each case (lower graph). (Adapted from Fernandez & G6ldberg, 1971, page 673)

The Motor System

The fine details of motor control are extremely

complex, especially in the higher animals where there is

an increasing contribution from central rather than local

sources. Every limb has a number of independent muscle

groups acting both as extensors and flexors and each

204


muscle consists of a very large number of separate muscle

spindles which themselves consist of a number of separate

muscle fibres. Each fibre can be influenced by electrical,

chemical and mechanical means and the nerves that take

information from and to these fibres branch in many

different ways, so that even within a spindle var ious

groups of fibres share some nerve paths but not others.

(de Vries, 1967; Thompson, 1975; Granit, 1970).

Many findings have been obtained from in vitro

investigations of animal preparations. Sufficient

important differences of detail between animals have been

observed to make the direct extension of these to humans

problematical. In the lower

the intrafusal spindles are

animals, such as amphibians,

innervated by branches from

the extrafusal musculature whereas in mammals there is an

increasing independence of the intrafusal and extrafusal

systems (Granit, 1970). In the former case it is possible

to account for such behaviour as posture in terms of a

spinal reflex response to stretch imposed by altering

loads. In mammalian muscles, however, there are

reflex-like movements which in fact depend on intrafusal

activity and which can be maintained in the absence of

extrafusal (alpha) output (Granit, 1970). The emerging

picture is one of an extremely elaborate automatic control

which is able to make constant adjustments to the

multitude of individual muscle fibres. The balance of

flexors and extensors by alternating the recruitment of

various semi-independent muscle groups is an essential

feature of smooth continuous operation.

Automatic and Volitional Control

The degree to which such systems are automatic, that

is they depend on changes due to direct interaction with

the environment, rather than volitional control by the

higher centres of the brain, is still an open question.

205


The greater complexity of the mammalian system with its

nerve tracts from the intrafusal spindles extending into

the lower brain stem and beyond makes single cell

recordings extremely difficult to interpret and these

difficulties are multiplied by the fact that all natural

movements are polyneuronal. In some systems, it is

possible to build up a fairly clear picture of the

contributions from the various parts of the nervous

system. Euler has proposed a circuit for the action of

the intercostal muscles during breathing that accounts

for in vivo performance when the air passage is

restricted. Control is shared between the spine,

respiratory centres and the cerebellum and it is evident

that since single inhalations and exhalations can be

voluntarily imposed there must also be indirect links

with the higher parts of the brain (Granit, 1970).

In an experiment by Basmajian et al (1965) a subject

learned to regulate the level of excitation from an

electrode placed in the abductor pollicis brevis of the

thumb. This was achieved by attending to visual and audio

feed-back. It is clear that volitional control of very

small muscular units is possible whatever the functional

implications might be. In general it seems most probable

that for well established actions such as breathing and

walking there is a 'proprioceptive elaboration of a

relatively simple central command alternating between

flexors and extensors.' (Granit, 1970) and that during the

learning process the higher brain functions interrupt and

redirect these established sub-systems to create new

'automatic' links which allow the new skill to become part

of the repertoire.

206

Bicycle Riding

Flexor muscle folds elbo .... PULLS BAR ~

No .... rist moyement~

joint free to rot8te

Extensor muscle str8ightens elbo .... PUSHES BAR

~ Trunk keeps

-- st8tion8r!l on bike

Figure 8.5 Showing the simple model for single arm control of the handle bar.

A Possible Control Mechanism

Chapter 8

Typical control movements are used with steering

wheels, boat tillers, aircraft joysticks etc., and take

the form of a tension in the appropriate muscle group and

inhibition of the antagonistic groups so that the control

mechanism moves to that position where the muscle tension

balances the mechanical torque. It is highly likely that,

in common with most human activities, individuals will

have a large repertoire of effective alternatives for

achieving appropriate control movements but in order to

compare the known capabilities of the motor-system with

the control demands some simplified model is needed.

Figure 8.5 shows a schematic layout for the proposed

operation of the steering mechanism. An informal riding

experiment was carried out in which the bar was held in

every strange way that could be devised. Clenched fists,

palms flat, back of the hands, finger-tips, wrists, lower

forearms etc. The only problem encountered was when

pushing or pulling very lightly with fingertips only. In

207


this position the body was deliberately held back to avoid

contributions from movements of the upper trunk. With

sudden turns it felt as though one of the hands was coming

off the bar which lead to a momentary wobble. When the

load on the bar was increased by leaning

fore ward depending on whether pushing of

effect disappeared.

backward or

pulling the

Thus it seemed that since the hands themselves were

playing no part in the operation either as sensors or

actuators it was reasonable treat them here as a single

unit together with the wrist and forearm. In order to

turn the front wheel the rider must alter the relative

distances from the tips of the handle bars to the saddle

and since it assumed that the lower trunk and legs do not

normally move for steering purposes this is the same as

altering the distances between the forearm extremities and

the hips. This movement could be aChieved in several ways.

The arms could be kept the same length and the upper trunk

swivelled, Or the trunk could be kept still and the arm

lengths altered by changing the angles at the shoulder and

elbow.

Although either arrangement is possible from the

purely mechanical aspect a simple experiment suggests

that the postural reflexes give a more restricted choice.

If one sits in a chair in front of a table and grasps the

edge with the arms slightly bent at the elbow in an

approximate imitation of the bicycle riding position

(figure 8.6), an attempt to rotate the upper trunk by

consciously changing the length of the arms produces only

a change in arm tension. In order to alter the trunk

position it is necessary to intentionally 'twist the body'

in which case the arms just follow the movement.

208


Figure 8.6 The simulated riding position.

If the chair is moved a little further back so that

the weight of the upper trunk is partly carried by the

table, as in the drop-handle bar position, the shoulders

can still be twisted voluntarily and, despite the extra

load they are now carrying, the arms move to accommodate

this change. Allowing one hand to slip suddenly from the

table edge leads to virtually no alteration in the trunk

position, the full weight being taken by changes in the

supporting muscles. This sudden shift of weight from both

shoulders to one must produce a twisting couple on the

upper trunk but no appreciable movement is noticed. This

implies that there is a well established reflex that

controls both the fore and aft and twisting movement of

the trunk to oppose externally applied forces. It will

therefore be assumed, in the interest of establishing a

simple model for discussion, that control of the bar is

effected by altering the tension in the elbow joint

muscles and that the forces generated are transmitted

entirely to the steering bar.

Also in the interests of simplicity it will be assumed

that control is exercised by pushing and pulling on the

209


bar with one arm only, leaving it open as to whether the

other arm passively follows or makes a similar shared

contribution. It may be noted in passing that, although

one-handed riding is quite normal, most riders prefer to

have two hands on the bar for difficult manoeuvres,

suggesting that there may be some operational difference

between one and two handed riding.

Resting Tension.

In the simplest of terms what is required for steady

dead-ahead riding at speed is a situation where the

muscles operating around the elbow joint are fully

relaxed, allowing the handle bar to follow the movements

of the autocontrol. However, it is necessary to propose

some slight resting tension in order that the muscles will

be in an 'alert' state to respond to control demands. This

stable tension is the 'tonus' of the muscle defined by

Basmajian (1962 p41) as ' .. determined by both the passive

elasticity or turgor of the muscular (and fibrous) tissues

and by the active (though not continuous) contraction of

muscle in response to the reaction of the nervous system

to stimuli.' Thus the flexor and extensor muscles will be

set at some steady low value which holds the elbow joint

at a particular angle in the absence of an external load

but which will allow movement under such a load without

the relative tensions changing. This slight resistance to

movement due to tonus will act as a high-frequency damper

in the steering system.

Muscle Control

The motor system has to fulfil three requirements.

First it must provide a stable platform from which precise

control movements can be made. Second it must apply an

angle-independent torque force to the handle bar to

produce a turn. Third, in the low autostability case, it

210


must move the handle bar so that its angular acceleration

continuously follows the acceleration in roll.

In animals with no independent neural circuitry to the

intrafusal spindles the 'stretch reflex' provides a crude

'constant length' device. The role of the mammalian

spindles in the control of muscle length is by no means

fUlly understood; but there is no doubt that the stretch

reflex to prevent changes in length is one of the

available functions. Without going into any greater detail

it can be seen that the requirement outlined here for

stabilizing the trunk is consistent with what is currently

known about the system.

When there is appreciable torque in the steering head

from the bicycle's autocontrol the requirement is for the

rider to allow this to operate and at the same time add a

further torque force for additional control. When the

elbow joint moves to accommodate the movement of the bar

under the resolved rider/machine couple the muscle lengths

will change. The length/tension ratio of the flexor and

extensor muscles must be set to constant values so that

their difference remains the same despite these changes in

length. That is there must be no stretch reflex.

All the early work on muscles encouraged the idea that

they achieved their postural tonus via a stretch reflex

mechanism. This meant that when a muscle had achieved a

set length due to alpha excitation any increase in length

caused by some outside force such as change in body

loading would automatically lead to the recruiting of

extra fibres to increase the resistance and hold the

position; Obviously such a system will not answer for the

purposes of bicycle control. Later research has shown that

in mammals at least the intimate control of the excitation

values in the main alpha neurons of the muscles is subject

to influences from both the intrafusal spindles and the

golgi tendon organs. The afferent output of the

211


intrafusals can be made selectively sensitive to length

and rate of stretch or inhibited by changing the values in

the static and dynamic efferents to these units. This

output can be directed to excite or inhibit synergistic

and antagonistic muscle groups remote from the detection

site. The input and output connections to the intrafusal

spindles have branches up to the brain and consequently

the motor muscles are no longer tied to a simple stretch

reflex. Response for various combinations of afferent and

efferent excitation can produce a great variety of control

responses.

As long ago as 1909 Sherrington reported a condition

in a decerebrate cat where the extensor (vastocrureus) of

the leg could be moved to various positions by the

experimenter. Previously it had been thought that limbs

would be either completely relaxed, in which case they

would fall back under gravity if displaced, or rigidly

held in some position against gravity, in which case

attempts to move them would lead to a stretch reflex

opposing the change. The condition observed by

Sherrington, which

fully explained

he termed 'plasticity' has still to be

but it is now apparent that the

independent control of the intrafusal spindles and golgi

tendon organs in muscles allows a large combination of

autogenetic and antagonistic activity which could account

for a condition where the reflex due to external

stretching was irihibited (Matthews 1972, pp 443-445). The

'alert' no-signal condition proposed in the paragraph on

resting tension above is similar to the plastic condition

observed in the cat preparation, although since the arm is

supported at handle-bar and shoulder the resting tonus

need be nothing like so great as that required to hold the

weight of the limb against gravity. Figure 8.7 illustrates

an experiment by Buller and Lewis on the length-tension

curves of the soleus muscle in the cat. The curve shows

212

Bicycle Riding

the change in

(abscissae) when

Chapter 8

tension (ordinate) against

the muscle was subjected to

length

a full

'tetanus' excitation (described in Granit, 1970).

t 1200 e n 5 i o 1000 n (gms)

800

length (mm) 4 8

---a-._a_a_a, a..--II .. II-II ........... _

12 16 20 24

Figure 8.7 The relationship between length (abscissa) and tension ( ordinate ) of the soleus muscle in a cat when subjected to full tetanus excitation. (Adapted from Granit, 1970, fig. 10, page 23)

The implication here is that if this muscle, holding a

load of say 1000 grams at a length of approximately 4mm,

was then shortened by some external force to 3mm then the

force generated would fall to 900grams and in the absence

of any other input would continue to collapse since it

could no longer support the initial load. If however the

same test was applied on the flat part of the curve

between 7mm and 20mm the tension would not alter and the

new position would be held. Of course this experiment

takes no account of what the antagonistic muscles are

doing at the same time, nor of the effects of altered

instructions from higher levels of organization as a

result of the changes in excitation of the fibre

afferent-s, but it does illustrate that the internal

organization of this muscle can exhibit the quality of

constant tension for changed length. Marsden et

213


al. (1971) describe an experiment in which an unexpected

opposition to the voluntary movement of a subject's thumb

was suddenly introduced. In the normal state this

resistance led to an automatic increase in the tension of

the driving muscle to maintain the intended rate. When

however the thumb was anaesthetised by local injection

there was a reduction in the rate of response, indicating

that the tension had not altered. This finding is usually

quoted as an instance of the contribution of the jOint and

cutaneous sensors to this sort of 'reflex' since the

muscle that does the driving is in the arm not the

anaesthetised thumb. However the point here is that the

subject is producing the kind of movement required by the

control model for the operation of the handle-bar. In the

case quoted the feedback seems to have been blocked by the

anaesthetic. In the case of the bicycle it would have to

be as a result of some sort of organized inhibition of the

spindles and/or golgi tendon organs.

Thus it can be seen that the human neuromuscular system

is capable of producing a constant tension in a muscle

independent of changes in length and that volitional

control over small isolated muscle units has been

demonstrated. This is sufficient evidence to justify the

claim that holding an angle-independent tension to produce

turns is consistent with what is known about the motor

control system.

The Roll Induced Movement

The final requirement is to produce a continuous

angular movement of the handle bar in response to the

vestibular output. There are many functions in mammals

that show a fine control of position which can only be

explained by independent spindle action. A good example

being provided by the demonstrations by Euler that the

desired 'tidal volume' of the lungs is controlled by the

214


length to which the intercostal intrafusal muscles are

stretched in breathing (in Granit, 1970) Thus the

essential neural connection to adapt the existing system

for roll-follow control is to take the rate of change of

excitation in the vestibular system caused by rates of

roll and apply it via some multiplier to the tension

values in the arm muscles. It is not intended to imply

that the implementation of such a link is in any way

simple. The extremely complex polyneuronal nature of any

limb movement is such that comparatively simple movements

in the large muscle groups must be translated into a vast

array of 'messages' to each of the individual muscle

spindles involved.

An experiment by partridge and Kim (1969) provides

an interesting observation of a very similar system

actually operating in the cat. They recorded the isometric

tension in the triceps surae muscle of a cat during the

sinusoidal excitation of the ampullary nerve bundles of

the vestibular system. Between a wide range of frequencies

the tension in the limb moved in sympathy with the

oscillation of the stimulus, with a conduction delay

of 15 msecs which is several times faster than that

observed in the human rider. This is exactly the sort of

arrangement required to operate the control model.

Comparison with Postural Control

There is a literature on postural control as distinct

from motor movement because to some degree posture is seen

as being controlled by local reflexes rather than a

centrally controlled organization. The problem is that

studies of posture in man show evidence of central

contributions and complex responses for simple bipedal

balancing tasks at latencies below the minimum recorded

for voluntary movement. Recording exactly what every limb

is doing during natural movements is extremely difficult

215


and it is all too easy to misinterpret local motion

because the whole action has not been captured.

Consequently it is usually very difficult to be quite sure

what role muscles are actually playing in a complex

movement. There is evidence that sequences of postural

actions are anything but 'dumb' local reflex responses,

but at the same time their speed of action at the lowest

level of the hierarchy argues that reflex like processes

are being recruited in the responses. Since learning to

ride a bicycle necessitates recruiting fast responses for

lateral balance it is very likely that there is a link

between standing postural control and bicycle control. The

proposal that pushes superimposed upon and temporarily

disrupting the underlying continuous balance induce

desired changes in lean

balance

blocks

during motion.

angle also speaks to

The sprinter on his

bipedal

starting

is so

represents an

far displaced

extreme example. The centre of mass

from the support point that only a

very high rate of acceleration will prevent a fall. By

disturbing the autonomous balance system the higher centre

of control forces a response which achieves its

requirement without further contributions. Two sets of

exploring the sequencing of

standing balance will be used

responses in

to illustrate

experiments

maintaining

some of the common points between the bicycle task and

posture control.

Nashne:r's Pll!ttform Tasks

Nashner (1976) conducted a series of experiments in

which subjects stood on a platform which could be

translated in the antero-posterior (A-P) direction and

rotated to give a 'toes up' (dorsiflex) or 'toes down'

(plantarf1ex) movement of the ankle joint either

independently or simultaneously. Changes in body sway and

the torsional forces applied by ankle musculature were

216


measured during platform movements. Nashner' s interest

was in the possible role of reflex responses in the ankle

for posture control. Seven of the twelve subjects made no

rapid compensation for the mildly disturbing changes

induced but brought in appropriate ankle movements after

about 200 msecs. These responses were considered to be of

visual or vestibular origin so the focus was on the five

who made fast reflex-like responses.

It was clearly shown that changes in ankle angle

induced muscle responses in the smaller group, even when

they were inappropriate and caused unwanted sway. When the

platform was moved backwards the subjects made a toes down

movement after a latency of approximately 120 msecs to

oppose the induced foreward sway. When the platform was

rotated in the dorsiflex direction without any translation

the subjects responded with a plantar flex movement which

was inappropriate and gave a self-induced sway backwards.

After three or four trials this reaction was adapted out

and then resumed when the conditions were altered to make

it appropriate again. This sort of reflex movement is

termed a Functional Stretch Reflex (FSR) as opposed to the

faster myotatic response, which has a latency of 45-50

msecs. No myotatic responses were recorded in any of the

experiments.

In his discussion the author proposes that both the

fast reflex action of the smaller group and the delayed

visual or vestibular response of the larger, fit into an

hierarchical model of postural control in which the

cerebellum exercises control over the gain of reflex

responses to achieve the desired effect. He quotes two

different models for the organization this control.

Welford (1974) suggested that the central process adapts

an internal 'model' of appropriate responses to cope with

unexpected changes whereas Pew (1974) suggested that when

faced with an inappropriate response the system suppresses

217


the existing action to give more time to assess what was

happening before producing a new response. Nashner

suggests that these two models offer possible explanations

of the difference between the fast responding and the slow

responding subjects with the slow subjects using the

latter strategy and the fast ones the former. Even when

one of the slow subjects was told exactly what was

happening he was unable to override the inappropriate fast

response, but it is of course quite possible that a longer

period of training might have allowed a conversion

eventually to the more flexible system. Several subjects

with deficits of the cerebellum were tested on the same

task and showed little ability to adapt their fast

responses in the inappropriate task.

These two models can be directly related to the problem

of learning to ride a bicycle. The point about the bicycle

task is that it appears on the surface to be a

navigational problem, like riding a tricycle, but it

carries with it a postural-like balancing element which is

intimately tied in with the former. When the rider first

tries to steer for direction only there is a strong out of

balance effect. It can be assumed that the initial

response will be that already established for postural

balance, in the same way that Nashner's 'fast'

moved their ankles inappropriately. That is,

subjects

the body

will be rotated away from the direction of fall in an

attempt to keep the weight within the support platform.

In many cases the outside foot will in fact be moved from

the pedal to the ground to ensure stability. The first

thing the rider must learn is to suppress this

inappropriate response and replace it with a handle-bar

movement into the fall. Once this has been established

the cerebellum can exercise its gain control of the arm

action to achieve an acceptable balance between stability

and power. The fact that Nashners' 'fast' subjects

218


suppressed the inappropriate ankle response in typically

three or four trials shows that such adaptation is part of

normal balance and goes a long way to explaining why

children can learn to ride a bicycle so quickly.

The difference between the myotatic and FSR response,

(70-75 msecs) presumably reflects the extra time needed

for the sensory pulse to ascend to the brain and the

instruction to return. The difference in the latency

between the slow and fast subjects, 200 msecs as opposed

to 120 msecs, seems to be a function of different basic

strategies and it is not necessary to assume that the slow

subjects would be irrevocably committed to such a latency

in different circumstances. That is once the connection

between the vestibular or the visual system has been well

established there is no reason why the latency should not

reflect the time taken for the one way journey from the

detecting site in the head to the arms. In bicycle riding

the information for driving the response comes from the

inner-ear Or the eye which, unlike the ankles in the

sources very near to the cerebellum. platform task, are

Consequently there is no need to allow time for returning

information. Partridge and Kim's cats, mentioned above,

had a system delay of 15 msecs, so there seems to be no

objection to the 60-120 msecs phase delay observed in the

runs. It is also possible that the difference in delay

between the two riders was due to a predisposition to

'fast' or 'siow' styles of response. Certainly the slow

responder was the more skilled rider of the two and had a

wide experienbe of other balance skills such as skiing and

surfsailing.

A later paper Cordo and Nashner (1982) provide further

evidence of activation of controlling muscles in both the

leg and the arm at latencies below that elicited by purely

voluntary movement.

balance system is

They also show that the postural

anything but an unadaptable local

219


reflex, and that the site of action can be switched

without practise when this is appropriate to maintaining

balance.

In a series of experiments subjects made arm movements

or reacted to arm pulls which on their own would have

upset the postural balance. By recording muscle activity

in the arms and legs on a common time base it was shown

that potentially disturbing arm movements were either

preceded by appropriate leg movements or were held at a

low level until the leg movement had been initiated. It

was evident from their findings that the instruction to

pull or push with the arm was interpreted in such a way

that activity in the legs was first recruited to 'set up'

the situation so that when the arm movement came it

applied the mass of the body to the point of application

rather than swaying the body out of balance. It was also

shown that when movement of the arm was more appropriate

to keeping balance the leg response was suppressed and the

arm moved instead.

Of particular interest to the proposed bicycle control

was an experiment where the subject stood on a platform

which oscillated 10 degs 'toes up' and 'toes down' in a

continuous 0.1 Hz cycle forcing the subject to make

compensating movements of the postural muscles to keep

balanced. At a signal the subjects had to pull or push a

handle mounted at waist level. Cordo and Nashner' s

interest was the slight increase in reaction time of both

the biceps and gastrocnemius muscles compared to the same

task when the platform was stationary. Although the

continuous movem~nt to maintain balance was in the leg the

superimposition of an additional burst of activity at a

mean latency of 127 +- 38 msecs is exactly the sort of

activity required of the arm in control of the

destabilized bicycle with comparable delay.

Another interesting finding was the way that balance

220


control was immediately transferred to the arm from the

leg when this was the most appropriate movement. Such

instant transfer of activity to a different site is

exactly what is envisaged during the initial learning

task. Cordo and Nashner's subjects already possessed the

necessary organization to select the arm as the

appropriate site of action. The naive bicycle rider

apparently does not and must learn it in the same way that

the experimental subjects had originally to learn theirs.

The voluntary response time from the biceps was

measured as 155 +- 37 msecs, but during the pull and push

trials this fell to 66 +- 12 msecs and 73 +- 24 msecs

respectively. This supports the earlier claim that when

acting as a coordinated system the response time of

muscles cah be much faster than the latencies which are

elicited by voluntary movement, and consequently it is

argued that the 60-120 msecs phase delay discovered in the

continuous roll/bar control of the destabilized bicycle is

quite in line with this class of movement delay.

Lee's Swinging Room

The final reference to the postural literature concerns

a set of experiments by Lee and Aronson (1974) and Lee and

Lishman (1975). In the first experiments the authors

induced inappropriate postural responses in standing

infants and later in adults. When a 'swinging room'

produced the sort of visual information usually associated

with body sway, even though no change in posture was

present, subjects tended to make compensatory movements

which led to loss of balance. This effect was stronger in

the infants but was also present in the adults to a lesser

degree.

In the second paper the authors concluded, again using

their swinging room apparatus, that vision was the primary

source of postural information for standing balance.

221


Subjects were induced to respond to room movements as

though their balance had been upset. In one experiment

the room was moved back and forth over a distance of 6 mm

in a regular sinusoid with a period of 4 secs. The

subjects were briefed to ignore any room sway but a record

of body movements showed that they were swaying with the

room even though they reported that they had not moved.

The paper shows a reproduction of the room and subject

trunk velocities over a period of about 50 secs. These

measurements were made from analogue pen traces and no

digitized version was recorded, however the phase

relationship between the two traces on the page is

correct. (Lee, D.N., personal communication).

It is obvious that the visual stimulus must have been

the relative movement between the room and the subject and

that the subject's movement as shown by the trunk trace

must be subtracted from the room movement to obtain this

relative motion. The events interact in a loop. The room

sways and causes the subject to induce a trunk sway to

match it as though there had been a postural change. This

at once effects the relative movement between the subject

and the room and leads to further changes. A casual

examination cannot tell us how much the vestibular system

contributes to the observed motion but the authors showed

that movement with the eyes shut was greater than the

movements induced by the room implying that the visual

information gives a greater accuracy in maintaining

balance.

There are close links between this balancing task and

the bicycle riding task. In both cases the underlying

action seems to be outside the conscious control or

knowledge of the subject. In the destabilized bicycle task

the vestibular activity appeared to be controlling the

handle-bar responses and in the postural task the room

movements appeared to control the body movements. In both

222


cases the control seemed to be almost direct. In an

attempt to learn more about the detail of the form of

control in the room swaying task the curves published in

the paper were used to obtain the relative velocity and

acceleration movement between the body and the room on the

same time base.

The Trace Differentials.

Simple measurements on the traces given show that the

trunk velocity has a mean phase lag behind the room

velocity 0 f 0.75 secs with a maximum of 1.45 secs.

However it is the relationship between the trunk movement

and the relative movement of the room which is the more

important so the traces were enlarged to double the size

on a photocopier and then digitized using a PMS Graphbar

sonic bit-pad. Approximately 300 sample points were taken

of each trace giving a density of about 6 points per

second, or about 25 points per wave. The two records were

registered by interpolating between points to give values

at equal step intervals. The trunk velocity was then

subtracted from the room velocity to give the relative

velocity between them and this curve was differentiated by

taking the local slope between the values immediately

before and after each point. These three curves are shown

on the same time base in figure 8.8. The X axis has been

expanded so only half the run is shown. We can see that

the relAtive velocity is a regular wave with the same

period as the trunk velocity with a phase difference of

about 90 degrees or 1 second. Since this is the

information driving the response it is, as expected, in

advance. The relative acceleration is much noisier and it

is not possible to know how much of this comes from the

rather coarse level of recording and transformation.

223

Bicycle Riding

trunk veloclty

relative velocity

relative accln.

10 secs

Chapter 8

Figure 8.8 Actual trace of the trunk movement caused by a gently oscillating visual stimulus. (Adapted from Lee &

Lishman, 1975, page 87).

Possib1e Contro1 Systems.

A closer look at what sort of systems might control

standing balance and be disturbed in the manner shown in

the Lee and Lishman experiments shows that the problem is

complex and leads to the caution sounded above about

drawing simple conclusions from the traces of trunk and

room motion. In order to explore possible control systems

the bicycle simulation was modified to reproduce a much

simplified version of the standing task. The following

dimensions were used to represent a typical person: weight

160 lbs with a rigid body 6 feet tall having the mass

evenly distributed along its length with the centre of

mass half way at 3 feet. The eye level was 5.5 feet and

all movement was assumed to be around

that in real life

the ankle joint. It

people have a much is quite obvious

wider choice of movements with which to respond to

locked the foot vertical imbalance. With the ankle joint

gives quite a large support base in the fore and aft

direction and any disturbing push would lift the toe or

heel and give a strong correcting couple. Movements of

the big toe provide a powerful couple very fast and it is

224


known that loss of the great toes in an accident does give

balance problems. It is very likely that the ankles, knees

and waist joints all act together in a synergistic

response which would have important effects on the way the

centre of mass moved in relation to the support point.

However the fact remains that very small movements of the

swinging room produced body sway responses so it is

evident that the subjects in the experiment were primed to

make active responses to disturbances and not just relying

on the passive stability conferred by a locked ankle

joint.

The problem for the standing person is this: any

displacement of the centre of mass from directly above the

support point leads to an increasing rate of acceleration

into a fall. The subjects in the swinging room experiment

only deviated 5mms either side of the upright so if the

height of the measuring device on their backs was about 4

feet they were only swaying through an included angle of

less than 0.5 degrees. Thus we can see that very small

changes are significant and the performance of the

simulation shows that it needs to be, if it is to keep

control. Any active control must first sense a fall and

then oppose it. The longer it leaves the correction the

more effort it needs. If it produces a much bigger

correction than is needed it will cause an acceleration

back over the zero position and then will be faced with a

worse situation on the other side. This will be repeated

in increasing oscillations unt il one fails to reverse.

Thus we can see that the problem is the same as that

encountered in the bicycle control. Discrete corrections

are far too unstable to be realistic, so the sensed rates

of movement must be fed back with a gain which is big

enough to contain any expected disturbance but not so

great as to produce a diverging oscillation. Any long

delay between sensing and implementation will increase

225


instability and therefore limit the amount of gain which

can be used. If only acceleration is fed back the velocity

will not be removed, if both the velocity and acceleration

are fed back then any angle which accumulates during the

operation will remain and this will lead to a further

increase in the falling couple. Stability is typically

achieved by actively oscillating about the zero point.

Control of limb joints must take place via changes in

length of muscles. Extensor and flexor muscles must work

in sympathy and movement is possibly specified by giving a

common set point at which the tensions are equal. However,

as far as the joint movement is concerned this is received

as a torque couple and that is how such changes were

modelled in the simulation. The movement around the ankle

was obtained by working out the weight couple from the

displacement of the centre of mass from the support point

and adding to it any muscle torque specified by the

control system. The room movement was modelled so that

relative movement between it and the person could be

found.

First the simulation was given a feed-back control

system which feel. the velocity and acceleration of the

trunk into the ankle joint opposing any fall. The gain was

trimmed so that it could restrain the natural fall to

somewhere the same as that seen in the experimental

traces, ie. about 0.25 degrees in one second. The

unrestrained fall rate will give about four times this

dispersion in the same time period over the same angle

range. Now the Lee and Lishman demonstration shows that

when the room moved the person responded as though he had

swayed so the control was changed to feed in relative

movement between the room and the eye position rather than

the actual body movement. The result was that initiallY

the control torque worked in the same direction as the

weight couple and an acceleration much greater than the

226


free fall case was the result. With the gain available

this system was unable to contain the initial fall and

went out of control at the first dispersion. If the gain

was increased so that the fall could be checked the system

became unstable going into an ever increasing divergent

oscillation. In real life it is evident that dangerously

excessive accelerations invoke a different level of

response, such as putting out a foot or raising an arm. In

any case the experimental subjects did not behave in this

way but contained the fall within 0.25 degrees.

Secs Relatiye Room accln. yeloc. yeloc.

16

14

12

10

8

6

4

Figure B. 9 Simulation of standing balance with trunk acceleration being driven by feedback of both vestibular and visual motion from the swinging room. A short pulse of 0.44 secs duration has been put in to the right at 9.0 secs.

Evidently what is needed is some sort of restraint on

the rate of actual fall induced by the false room

information. The vestibular system would not be subject to

the deceptive movements of the swinging room but would be

measuring the actual fall and thus could be a suitable

source of information for such a restraint. The question

then is, what happens if the control is fed both the

visual and the vestibular changes? This is where the

227


model comes into its own as it is certainly impossible to

visualize what the effect of mixing the two inputs would

be on the control output without one.

Figure 8.9 shows the output when the true velocity and

acceleration in fall is fed into the control together with

the relative velocity and acceleration due to the

deceptive room movement. The result is a controlled trunk

velocity with the same period as the room velocity which

is exactly what we see in the real traces. The delay

between these two in the simulation is about 0.5 secs as

opposed to the actual mean lag of 0.7 secs but this can be

increased to the same value in the simulation by

introducing a delay into the control routine.In both this

and the bicycle simulation it was demonstrated that

putting velocity and acceleration information into the

control leaves any accumulated angle untouched. In the

bicycle case this left a residual turn, which is stable,

but in the standing balance case it leaves and angle of

lean which produces a disturbing weight couple. Since the

simulation is controlling on velocity and acceleration

only, the angle gradually accumulates as can be seen by

the way the mean of the vertical angle trace in figure 8.9

is moving gradually left.

The human can easily alter the relative position of its

parts to achieve a change in the relationship between the

total centre of mass and the support point, something the

simulation has no power to do. However another method of

dealing with residual angles is to do what the bicycle

riders did and put in a short push pulse to oppose them.

Just to emphasize that a short push, such as might be

administered by a rapid movement of the toes, will have

the same effect as it did on the zero-stable bicycle, a

single pulse lasting just under half a second has been put

in at the nine second mark, and is shown by the arrow.

This added pulse pushes the mean of the vertical angle

228


oscillations back towards the zero line but leaves the

basic characteristic unaltered.

In the actual trace the trunk velocity has a definite

tendency towards a triangular shape. It could be argued

from this that the underlying control is putting in a

fairly steady rate of acceleration between peaks and

changing sign rapidly at each of them. If this was the

form of the control then the focus of interest would be

what unique events occur in the stimulus immediately prior

to the sign changes to cause them. Candidates here might

be the rising relative velocity which triggers the change

when it exceeds some threshold value Or possibly the rise

in the relative acceleration although this trace is much

messier and therefore less unique. Secs Trunk Relative Room

angle veloc. veloc.

4

3

2

1

Figure 8.10 Simulation of push control for standing balance as described in the text. Trunk angle varies between plus and minus 0.3 degrees. The original room velocity has been put in for reference.

However there are a number of difficulties which appear

when such a system is run on the simulation. Attempts to

control by pulse inputs alone lead to diverging

oscillatory instability. It is certainly possible to keep

control by imposing short pulses on an underlying

229


continuous feed-back whenever some angle threshold is

exceeded. Figure 8.10 shows this working with pulses of a

nominal value of 4.5 applied over a period of 0.36 seconds

whenever the vertical angle exceeds a set threshold value.

The difficulty is that the period of oscillation cannot be

much increased without losing control. The period of the

real trace is 4 seconds with an angle dispersion of about

0.3 degs. In figure 8.10 the initial fall to the left

under the restraint of the continuous feed back is at

about the same rate and reaches about the same angle. At

this point a push which is strong enough to make the

angle cross the centre line immediately reduces the period

to about 1 second as shown in the figure. If it is reduced

until the initial rate of reversal is nearer to the

recorded 4 secs period then the centre line is never

reached. If the length of the pulse is increased in an

attempt to keep the reversal going there is an interaction

between the contihuous feed back and the long pulse and

the trace starts oscillating about a mean angle which

again does not cross the centre line. Only short pulses

can be used to influence the continuous system without

altering its basic characteristic. The inability to

increase the wave period is due to the natural frequency

of the oscillation of the trunk about the ankles assumed

in the model. As has already been mentioned it is possible

that a correlated movement of the body sections might make

large changes to the effective radius of gyration and thus

alter the natural frequency. It is evident that more data

would be needed before a model which might produce a

solution could be constructed and at present the

triangular shape of the trunk velocity remains

unexplained.

Although the model is a very simple one it does help us

to understand several interesting properties possessed by

such a system. If the natural control achieves this sort

230


of stability by locking the ankle joint and relying on the

passive stability of the foot it would not have responded

to the swinging room. Active balancing of a standing body

around such small angles as half a degree displacement

involves almost inevitably some sort of continuous feed

back about the rate of sway. If there is too much power

the characteristic will be a diverging oscillation. If, in

the swinging room experiment, it is supposed that the

subject is under the control of visual information only

then a gain appropriate to normal conditions would be

unable to contain the sway induced by the false movement

of the room. It further shows that if the conflicting

information of both the vestibular and visual channels is

added together so that both are making equal contributions

then the behaviour of the model in the presence of the

swinging room is in many respects the same as that of the

actual recording. A much more detailed record of such

movements would be necessary before a similar analysis to

that done on the bicycle could be carried out but in the

interim it can be stated with some confidence that

standing balance control seems to face the same class of

problem as that for riding the destabilized bicycle and

that as far as can be judged from the rather sparse

information given in this paper humans set about solving

this problem in much the same way using the same basic

neural equipment.

The aim of the bicycle study was to find out the

minimum conditions necessary for control and because of

this the trials were carried out with the subjects

blindfolded. Unfortunately lack of time prevented any

trials with sighted subjects so no comparison is possible

as a series of cal ibrated runs wou ld be needed to

determine whether there was any difference in the angle

control when visual information was available. However

the general performance of the riders seemed exactly the

231


same under blindfolded or sighted control and a study of

wheel tracks showed the same short and long period

oscillations were present under both conditions so it

looks as though a continuous input for angle is not used

when sighted. It would however be very interesting to be

able to ride a bicycle within a large swinging room to see

if the resulting performance was consistant with the

visual information replacing Or combining with the

vestibular input. All that can be said for sure from the

bicycle experiments is that loss of vision caused a

minimum of disruption to the established sequence of

responses and surprisingly did not 'feel' subjectively any

more difficult than normal riding. On balance this

finding together with the analysis on the Lee and Lishman

data suggests that the vestibular and visual information

are both available and under normal circumstances will

both give the same input. The complete loss of one leads

to the other taking over but the distortion of one in a

'deceptive' manner leads to an output which is consistent

with an addition of the two inputs.

Summary

The model proposed for control of the bicycle requires

that the upper trunk of the rider is held in a constant

relation to the lower trunk and consequently the machine,

during control movements. The arms must produce either

steady angle-independent tension loads on the handle bar

for turns with full bicycle autostability or short period

o%ff pushes when this is weak or

supply a continuous movement

absent. They must also

following the roll

acceleration when machine autostability is below some

threshold value on which the directional pushes are

superimposed. Although none of these functions has been

demonstrated specifically for the bicycle, it is argued

that the system as understood at present clearly has the

232


capacity for all three and that the sensory and motor

performances revealed in other balance tasks is of the

same general type as that required for the successful

performance of the proposed bicycle control.

233


9. THE ORGANIZATION OF CONTROL

Introduction

The enquiry so far has shown in some detail how the

handle bar of a bicycle is moved to achieve control. This

knowledge will now be related to the existing theories of

motor skill, already discussed in chapter one, to consider

how the rider might achieve control in terms of internal

organization.

The Essential Ingredients of Control

Because the bicycle is so unstable only a very limited

number of systems will satisfy the control requirements.

The autostability built into the machine by virtue of its

design removes the need for any additional inputs to

achieve basic roll stability when travelling over some

critical speed. In this condition an angle-independent

pressure on the handle bar produces a stable lean

proportional and in the opposite direction to the push.

This results in a turn in the direction of the lean and

proportional to it. Upright running is restored by

removing the pressure. Transient disturbances, such as

surface irregularities, will lead to changes in the

direction of running but roll divergence will be

automatically removed. Steady disturbances, such as side

winds, will lead to corresponding turns which can be

countered by a continuous pressure on the appropriate

handle bar. Anything which interferes with free rotation

of the steering head under the influence of the

autostability torque will cause loss of roll stability.

As the speed falls below the critical value the

autostability forces will fail to contain roll divergence

234


and unless prevented the bicycle will fall into a turn to

one side or the other from which it will not recover.

There is a transient range of speeds within which the

autostability response can be enhanced by rolling the

frame in the direction of fall. Frame rotation is induced

when the upper part of the rider's body is rotated in the

opposite direction, that is against the fall.

At very low speed the autostability fails to make a

significant contribution and in the absence of any other

inputs the bicycle will fall rapidly in the direction of

the first roll departure. In this speed range riders

are observed to move the handle bar angle at a rate which

is a multiple of the roll angle, with a short phase-delay.

The essential difference between this and the machine

stability control is that it does not respond to absolute

angle as well as roll rate. The consequence is that, in

the absence of any further control inputs, lean angle

errors will accumulate causing the bicycle to go gradually

into a turn from upright running.

The absence of continuous absolute angle control and a

longer delay in the human system, also leads to a

difference in the effect of directional control movements.

An attempt to use the steady steering pressures described

above will give a rapid increase in roll rather than a

steady turn. Directional control is now achieved by

single short-period pushes, timed to allow the rather slow

response to take effect. A single push produces an

oscillatory rate of roll away from the side of

application. A moderate push will reverse this and send

the mean of the oscillations back towards the upright from

where it will gradually oscillate either back down in the

same direction or over on the other side. Straight

running consists of a series of gentle oscillations about

the upright at the natural frequency of the system, with a

restoring push whenever the lean angle exceeds some

235


threshold value.

Navigational control, that is steering the bicycle in

relation to the environment, must always entail movements

via the control systems described above. In normal

conditions a turn will be demanded by a continuous push on

the side opposite to the desired turn. In the low speed

case this must be modified to separate start and stop

pushes. In the abnormal case of 'no-hands'

is effective only on bicycles with good

riding, which

autostability

characteristics, a turn is achieved by a strong roll of

the upper body away from the desired direction of turn.

Even when riding normally such body leans will enhance any

existing autostability forces. Apart from these

limitations, navigational control poses the same problem

as that found with other vehicles and is not part of this

study.

The Applicability of Existing Theories

The relationship between existing theories of motor

performance

riding will

and what has been discovered about bicycle

ndw be considered. There seems to be no

objection to applying a stimulus-response interpretation

to the basic zero-stability control loop. The continuous

change in the controlling muscles follows the vestibular

output without interference from any higher level. The

steering pushes do not replace it but are added to it. A

stimulus-response view might also be applied to the

apparently automatic removal of lean during straight

running on the destabilized machine. Whenever the angle

of lean reaches a particular threshold a recovery push is

initiated, one state leading automaticallY to the next.

This theory is not very helpful when the initial

acquisition of the skill is considered nor is it any use

when considering why a steering push is introduced for

navigational purposes.

236


Motor Programs

An open-loop motor program approach cannot deal with

the intimate relationship between roll acceleration and

bar response in the destabilized control loop. The

bar rate follows the roll rate in detail and the

continuous feedback of roll rate is essential. Both the

continuous and short-period steering pushes superimposed

on the underlying system for turn control appear to be

stereotyped open-loop events but the automatic removal of

lean during straight running with the destabilized machine

must depend upon feedback.

Schema Theories

The difficulty with fitting schema theories to specific

functional models is, as already mentioned in chapter 2,

that they are descriptions of how information is behaving

and do not prodUCe as their output variables which can be

directly interfaced with the physical system. Schema

theories are really aimed at explaining motor learning but

since this must include descriptions of the behaviour

which is learned they must be capable of reconciliation

with the observed details of such events. The ability of

schema theories to explain learning depends on a high

degree of central control for both open-loop and

closed-loop systems. There are however several versions,

some more extreme than others, and interpretation depends

on the specific details.

Schmidt (1976, p.46) originally committed himself to a

minimum limit of 200 msecs for centrally controlled

closed-loop events which will not do for the destabilized

bicycle control. However he more recently (1980) accepted

the mass-spring view of muscle activity in joint movement.

This holds that the position of the joint is controlled by

the specification of the length/tension ratio between the

237


agonist and antagonist muscles and as such rejects the

idea of intimate central control at the level of

individual

position.

muscle groups which certainly eases the

Adams (1976, pp 96-97) rejects the proposed

kinaesthetic response time of 119 msecs for

closed-loop control and quotes studies which show

cortical responses to peripheral stimulation of 4 msecs in

monkeys. Given this sort of speed there might well be time

for some sort of central contribution during the observed

60 msecs delay in the basic loop. The degree of

contribution is of course open to speculation but this

timely warning is sounded by Fernandez and Goldberg (1971,

p.672): Can it be argued that the central nervous system

plays (only) a minor role in the dynamic properties of all

vestibular reflexes? One need only consider the

vestibulo-oculomotor system to be disabused of this

notion. The fast phase of nystagmus is unquestionably of

central origin. Even the dynamics of the slow phase

cannot be explained on the basis solely of peripheral

mechanisms. Thus it can be seen that even when dealing

with highly constrained peripheral activity it is not

possible to make a simple central/peripheral division of

control.

The central contribution referred to by

Goldberg is rather different from that

Adams. The former intend that, since

Fernandez and

envisaged by

the purely

mechanical properties of the vestibular system as a

transducer cannot completely account for

neural output, there must be some

the observed

additional

transformation, possibly at a central location. Adams sees

the sensory outflow as giving the central control a

knowledge of results, or ongoing report on the success of

the overall action, whiCh is not appropriate to the

destabilized control loop. There is a confusion here

238


between two separate feedback control loops.

The inner loop has roll rate as its controlled variable

with a desired value of zero. The manipulated variable is

the angular rate of the handle bar. The measured variable

is the rate of roll with a reference value of zero.

The actuating signal is the difference between the

reference and the measured variable, that is, the activity

in the vestibular output. Although this is often called

the errOr signal, this terminology is discouraged by

control engineers as the errOr in the system is the

difference between its present state and the desired value

of the controlled variable (Healey, 1975). Thus it can be

seen that the inner loop controls the roll rate about the

desired value of zero by applying some function of the

vestibular output to the handle bar. Because of

inefficiencies the roll rate is never held exactly at zero

and consequently there is always an actuating signal

present. This is not however a measure of errOr for the

system as a whole.

controlled variable

around zero. Thit

falls over. It

The system is in error when the

(roll rate) is no longer averaging

is, when it departs and the bicycle

is this latter information that is

appropriate to Adams' 'error feedback' value. The central

control is only concerned with failures to achieve a mean

balance. It is not concerned with the local variations in

the actuating signal which are just an essential aspect

of its correct functioning.

The next outward loop can be analysed in the same way.

Here the controlled variable is direction of travel, the

manipulated variable is still the bar, and the measured

variable will be the optic flow, sensed centrifugal

pressure or an integrated form of the horizontal yaw. The

reference, depending on intention, will be turn ~eft or

right, hard or gent~e etc. Control will be monitoring the

actuating signal, that is the measured variable minus the

239


reference. The central system, again in the terms of

Adams' model, is concerned with the error between the

desired direction of travel called for and the one

actually achieved. This time it is the turn which is the

by-product of the system's functioning.

When put like this it will immediately be appreciated

that it is much easier to specify the structural

correlates of the feedback for local control than that for

the central process. Hardly any modification of the direct

vestibular output is needed to account for the follow-up

action of the arm muscles controlling the handle bar. How

the activity in the afferent pathways from the various

sensory neurons that are stimulated during riding is

interpreted by the brain as constituting a failure to

achieve the intended goal is a very different matter.

Nothing that has been done yet in psychology or

neurophysiology comes anywhere near hinting what such an

activity might mean in structural terms. We return to the

lack of a theory to handle the interface between

information and structure.

Mass-spring Theory

The mass-spring theory states

adjacent skeletal units about

that the position of two

a joint is completely

specified by the ratio of the length/tensions of the

opposing muscles which control them. The great advantage

of this representation is that a controller wishing to

move a limb to a position in space does not need to

specify what trajectory is taken to get there. By

dramatically reducing the possible degrees of freedom in

this removes, at a blow, at least one of the nightmare

areas of potential combinatorial explosion that haunt

central control theories. A number of studies have shown

limb movements which closely follow the predictions of

this model (Kelso et al., 1980; Bizzi, 1980 and Schmidt,

240


1980) .

Applying the mass-spring idea to the two levels of

motor movement in the bicycle rider seems to present no

problem. The theory envisages control by two variables.

The length/tension ratio for opposing muscle groups and a

stiffness value (Cooke, 1980). Bizzi (1980) presented

evidence that the start position of the limb in relation

to the body was needed for accuracy. If relative limb

position is normally known then setting a length/tension

ratio appropriate to the existing position of the arms

wi th a low st iffness value would give the required

readiness condition for riding the autostable bicycle

discussed in the previous chapter. Controlling the

length/tension variable with the vestibular output would

produce the muscle length accelerations implied by the

destabilized bicycle observations. In other words this

gives the same effect as the simpler arrangement proposed

in chapter 8 where the agonist muscle is excited and the

antagonist inhibited.

A high stiffness setting does not alter the

length/tension ratio which dictates final position, but it

increases the amount of force involved in any movement.

It has already been shown in chapter 6 that the longer the

delay in the destabilized follow-up control the lower the

gain in the response must be to prevent instability. In

the opposed spring model gain equates to stiffness. That

is a change in the stiffness variable will give

accompanying changes in power of response for the same

vestibular output.

The single control pushes in the zero-stable system

would be achieved by adding to or subtracting from the

existing length/tension value. The angle-independent

pushes held for the duration of a turn in the autostable

system are not quite so easily accounted for. If control

must be exercised through only the two given variables

241


then an approximately angle-independent tension over a

restricted arc of movement could be achieved as follows.

The length/tension (limb position) ratio is set

appropriate to an angle well clear of the existing one.

That is one that will never be approached in practice

because of the response from the autostable torque. Now

the stiffness value will dictate the tension and since

there will be little change in length over the range of

angular movement this will be approximately angle

independent. That is for any turn the length/tension

variable is set at the same value with the stiffness

variable controlling the amount of push.

Coordinative Dissipative Structures

Kelso et al. (1980) address the specific problem of

relating the dissipative structure theory to the

mass-spring concept of limb musculature. The most

important change from the mechanical model is the implied

difference in neural organi zation. The mass-spring

analogy treats opposing muscle groups as single springs

whose tension-to-Iength properties can be used as a

control variable, together with stiffness and possibly

viscosi ty. (Note: - Sti ffness is the force required to

change the length of the spring. Viscosity is the

resistance depending upon the rate of movement) A

mathematical or electrical analogue will give a

performance that is very similar to the dynamic

performances observed in animal limb movements. Although

it is not explicitly proposed that the similarity extends

to the details of structure, mechanical models encourage

the idea that the complex neural system is organised in

such a way that all the fibres associated with one muscle

unit act together under the control of a single efferent.

Individual muscles are then seen as being coordinated in

the same way as the springs in the model.

242


A coordinative structure view is quite different. Here

the primitive units are the individual muscle fibres.

These are interconnected via a neural system which is no

longer considered in terms of afferent/efferent function

but takes the form of a complex interactive network. The

changes at a sensory ending are fed to motor plates on

neighbouring fibres to produce an unspecified general

interaction which gives the whole limb the properties of a

conditionally stable thermodynamic engine. Control inputs

change the non-dimensional 'essential variable' (see

chapter 2), modelled in the mechanical version by the

length/tension value, which leads to stable states which

equate to final limb position. A non-essential variable,

modelled by stiffness, controls the force available during

the movement.

The above concept seems to fit bicycle control rather

well. The study by Partridge and Kim (1969) demonstrated

that a regular wave form in the vestibular output led to a

similar response in the forelimb of a cat. This capability

is all that is necessary for the stability loop of the

bicycle control model. In chapter 8 a mechanical model

was used for the purpose of discussion but a dissipative

structUre model will do just as well. No one has yet

shown how the fine detail of innervation in the muscles

does actually produce the observed results, so both

mechanical and coordinative structure models are equally

possible.

One advantage of the dissipative structure is that it

constrains the degrees of freedom at the local level

making the control problem for the next hierarchic level

that much easier. This feature does not have such a large

impact on explanations of the mature control system since

bicycle riding was specifically chosen because it

dramatically limits the degrees of freedom of the rider.

But the autonomous nature of the dissipative structure has

243


considerable significance when considering the problem of

skill acquisition. The ab initio rider is faced with the

problem of how to move the bar to achieve control. The

mechanical model allows considerable freedom of bar

movement. It can be accelerated, moved at a steady

velocity, moved continuously or discontinuously in jerks.

Learning implies selecting just the right sort of movement

out of all these and there is the temptation here to

resort to prior knowledge at a higher level of

organisation to assist this choice. The dissipative

structure model requires control to be exercised only via

the essential variable, thus constraining the possible

responses. In this view the rather limited response

possibilities of the biological structure happens to

include one which allows bicycle control. Encouraged by

the experience of others that he too possesses this

ability the beginner runs through the limited repertoire

of responses in a trial and error fashion until some

degree of control results.

Internal Organisation for Bicycle Control

The bicycle was chosen because it is a very

constrained system. Once the exact way in which the

machine behaves during free riding is known it is possible

to say a good deal about the behaviour of the rider. It

makes sense to divide riding skill into two levels which

though similar are distinct. The skill of riding a machine

with high autostability is confined to producing torques

on the steering bar proportional to the amount of lean and

therefore turn. In addition to the above a rolling motion

of the upper body will cause the autostability to produce

a turn against the lean. Motorcycle riding is of this

sort at normal speeds. The skill of riding a machine with

either very low or zero autostability has two components.

First the handle bar must be oscillated at a rate that

244


follows very closely the oscillations in the lateral roll

sensors. Second short pushes on the steering bar produce,

after a short delay, oscillatory rolling velocities away

from the push.

It will be seen that this system divides into several

levels of control arranged in an hierarchy. At the lowest

level is the autonomous loop which keeps the movement of

the handle bar following the roll rate. Although, as has

already been discussed, it is possible that the

transformation of the vestibular output may require some

function that is contained in the central nervous system

this is not meant to imply that an external variable is

introduced from that direction. The loop is completely

self-contained and continuous and other control inputs

must be added to it without interrupting its operation.

Above this level lies the push-control. Its method of

application is to add a short ballistic pulse to the

handle-bar. The evidence in chapter 6 shows that this

control is applied automatically in straight running when

the lean angle exceeds some threshold value. Unlike the

roll response from the vestibular system the recovery from

unwanted lean is complex, particularly when there is no

direct information of absolute lean angle from the visual

system. Since subjects reported being unaware of making

this correction and had been instructed not to bother, it

seems reasonable to postulate a semi-autonomous loop which

monitors lean and then applies a correcting pulse when a

limit value is exceeded. This loop must also allow for the

slow response to avoid unstable overcontrol. It must be

open to higher control when an intentional turn is to be

made.

Lean angle must be judged from activity in various

sensory channels but how this is integrated is not known.

There are no theories at present which offer structural

correlates for such functions. Thus the descriptive level

245


has already moved away from the structural mechanical to

the informational. The loop for the lowest level,

described in the

electro-mechanical

previous paragraph, is

energy flowing from the

seen as

vestibular

system, down a motor neuron and into the upper arm

muscles. The loop described here is a notion to show how

activity at one site must inform activity at another. The

bicycle model does at least show how the informational

level is interfaced with the structural level. 'Give a

pulse, left' is a typical output of the information loop

and a down-flow of electromagnetic energy in the motor

axon appropriate to a sudden push is the input for the

muscle structure.

The control when autostability is operating requires no

lower level loop. Because the machine loop is much faster

and more powerful than the human loop, this need not

necessarily be 'switched-off'. It could remain 'on-line'

but dormant through lack of an actuating signal. The

control pushes for lean must be added to the autostability

torques by being angle-independent over the range of

movement. Schemes for either the mechanical or mass-spring

system have been indicated. These are not short pushes

but are held on for the duration of the turn and the

question arises whether they are open-loop or closed-loop.

If the pressure is applied very slowly the machine

response is almost dead-beat and therefore it would be

possible to use the feedback rate of entry roll to central

control to time when the push should be checked. Assuming

a minimum decision-time of 200 msecs would not cause a

problem at the slow rate but might with fast entry rates.

However such a scheme puts extra loads on central activity

and since rate of turn equates with tension there can be

an open-loop demand directly for the required rate of

turn.

Because the autostability removes absolute lean angles

246


there is no need for the second control level postulated

for the zero-stability condition. Since it must be

switched off for navigation purposes in the latter

situation then it seems to add no further burden if it is

also switched off when autostability is present.

Both systems require some sort of interface between the

purely navigational level and the levels of operation

described above. This has to change the navigation output

instructions of 'go left', 'go right', 'turn hard', 'turn

soft' into steady pushes for the autostable case and pulse

pushes for low stability conditions.

Learning and Development

Learning to ride a bicycle almost always entails

attempts to ride at very low speed, often with poorly

designed machines, and frequently on bad surfaces. Under

these conditions autostability is at best very weak. It is

therefore evident that most people need to learn the

zero-stability skill first and this seems consistent with

the observation that most bicycle riders can control their

machines at very low speeds. Before any attempt to ride

is made it is evident that the candidate already has the

essential ingredients of success. Control of muscle groups

via vestibular and ocular responses to short period

angular accelerations is a vital part of bipedal balance,

so the general class of event required by the bicycle

control model will already be in existence. Accurate rate

movements of the arms will also be a part of the normal

repertoire. The candidate will have watched others riding

and formed some idea that control is associated with

movements of the handle-bar. On the negative side, most

children have considerable experience with tricycles and

outrigger bicycles before attempting single-track riding.

This teaches them a use of the handle bar which is quite

inappropriate and presumably makes acquiring the new

247


control response mOre difficult.

Anyone who has watched a child learning to ride a

bicycle will be aware that in the initial stages they

induce large roll rates with bar movements which lead to

loss of control. These are almost certainly the result of

trying to control direction in the same way as they would

a tricycle. The next stage which follows quite quickly is

overcontrolling, where incipient falls are checked with

correct bar movement but so strongly that an even greater

fall results on the other side. After several diverging

wobbles control is lost. At this stage it seems that the

rolling effect of the bar is taking priority but the rate

of application is gross. In effect the emerging balance

loop is there but the relationship between lag and gain

is wrong.

It is usual at this stage for the instructor to hold

the back 6f the saddle and run with the machine. This

constraint can correct the effect of over vigorous bar

movement and the increased speed improves the response.

Typically, short runs of several seconds are observed

where the i.obbles die down and quite smooth control is

achieved. The trick is to let go during one of these

smooth patches without letting the child know! As soon as

he realizes he is no longer supported he starts

overcontrolling. At some point along the way the roll rate

sensed by the vestibular and/or ocular system has started

to exercise direct control over the arm muscles in the

short delay stability loop. Like many movement skills it

appears suddenly, sprite like, out of the blue only to

vanish as soon as it is attended to. Practice lures it out

again and eventually leads to its permanent capture.

A slow verbal stage of learning does not seem

appropriate for bicycle riding. For a start the basic

control loop will not tolerate slow operation. If the

phase slips much more than 100 msecs it gets out of

248


synchronization with the natural frequency of the system

and starts to enhance error, not reduce it. Secondly in

general very few bicycle riders realize how they operate

the bar for control. In the survey of ten riders referred

to in chapter 3, none of them had a correct understanding

of the necessary control movements so either they have all

changed their minds since learning or their verbalization

would have contradicted the actions necessary for success.

When one compares the time to acquire the basic skill

with the enormous amount of practice required to perform

some of the more exotic BMX tricks,

believe that the essential event

one is encouraged to

which discriminates

between not having and having riding skill, is something

quite simple. Cordo and Nashner's (1982) subjects

transferred postural control movements from leg to arm

instantly when it was appropriate showing that a facility

for rapidly connecting oscillatory activity at one neural

site to another already exists. Here is another

possibility for reducing the degrees of freedom. Say for

instance that the body was internally aware of which sites

were receiving some sort of regular wave stimulation. In

this case the arm muscles controlling the bar are already

the focus of interest so the attempt to succeed consists

in feeding the activity from each prospective sensory site

in turn to the site controlling arm movement. In the

bicycle learning case we can see that there will not be

many sites so stimulated. Providing we see the lower

level of arm organisation as something like the

mass-spring system then application of the correct wave

form, that is the activity in the rolling plane, will

produce approximations to the correct control movement.

This is then trimmed by altering the stiffness variable in

a direction that gives improved control.

Control of direction grows out of the realization that

every time the machine leans over it turns as well.

249


Control movements which lead to leaning also lead to

turns. Sudden pulse inputs to the bar cause a departure

in lean.Trial and error will lead to the discovery that a

short push causes a wObble away from it and that in

wobbling the machine turns as well. It is interesting to

note that the whole system, bicycle and rider, can be

described as a single conditionally stable thermodynamic

engine 'down-wind' of the control instruction set

'turn-left, turn-right, go straight'. All the individual

events react with each other to produce the three end

states which are selected from the centre via the

essential variable, whatever that might be. Fascinating

though this idea is, it does not in itself help in

explaining what is happening. However, it sounds a warning

that insufficient is known about the details of the

structure to be able to indicate which dynamic model best

applies.

Future Developments.

It is not easy to see how the bicycle experiments might

be developed to provide any immediate short term useful

function. The discussions in chapter 8 showed that it is

almost certain that at the lower level fast reflexes are

being recruited by the central organization to produce the

angle/follow response in much the same way that Nashner

and Lee showed fast unconscious ankle responses to

maintain, or in the latter case disrupt, a standing

position. Whether these are more thoroughly exposed in the

bicycle riding task from the clinical view or not is open

to question, and, since it involves the problem of

relaying information during extensive movement it is

unlikely that it offers any advantage as a means of

diagnosing defects in this class of function. However

useful or otherwise recorded bicycle riding might prove as

a clinical tool, there are still a number of questions

250


surrounding the control problem which would certainly be

very interesting to clarify from a theoretical point of

view. First a repeat of the destabilized runs without a

blindfold would clear up the question whether riders take

advantage of the absolute angle of lean available through

the visual

they were

system to modify the

blindfolded. Then

push control observed when

a set of runs with a

manoeuvring task on both the destablized and the normal

bicycle, sighted and blindfold would further unpack the

higher level of the control hierarchy. Standard runs with

a large number of subjects would allow an informative

comparison of the derived values such as lag, wave-period

and wave area, and highlight any personal idiosyncrasies

in control strategies.

Probably the most interesting single discovery is the

way the riders exercised control of the lowest balance

loop by disturbing it rather than changing the zero set

point which would certainly be the choice in a man-made

system. The example of the sprinter on starting blocks was

quoted as an indication that this sort of control exists

at some level in running balance control, and it is also a

fact that horse-riders, at the show jumping level at

least, force the horse to turn by shifting their weight to

one side to upset lateral balance.

During learning a self-contained bottom level loop is

set up by some form of central control similar to that

which allowed Nashner's subjects to select the arm as the

most profitable site of action rather than the leg when

this dynamics of the experiment were altered. This runs

continuously with fast reflex-like responses, more or less

under the direct control of some relevant analogue output.

The next level above superimposes disturbances which

disrupt the equilibrium at a lower level but by doing so

provoke the required response as

to restore the balance. More

251

the autonomous loop works

immediately profitable


perhaps than extending the inquiry further into specific

bicycle riding skills would be to extend the recording

technique to a number of other balance movement skills,

such as roller-skating, grass-skiing and wind-surfing to

find if a similar autonomous roll response loop lies at

the bottom of their control hierarchies. Such knowledge

would certainly be of interest to sports scientists and

coaches and indeed anyone whose task it is to teach people

movement skills. Being unconscious, such movements cannot

be taught directly by briefing and self-monitoring.

Somehow they are learned quite suddenly under the stress

of the demand and once established their presence seems to

be quickly forgotten. It is also possible that this method

of organizing the control hierarchy might extend to skills

not immediately connected with the sport applications

mentioned above such as manipulative tasks. Where skilled

movements have this form of control then it should be

fairly easy to isolate responses at the two distinct

levels and thus diagnose whether a patient was

experiencing

higher level

together.

difficulties at the reflex level, the

or in the synchronization of the

Conclusion

next

two

An interesting by-product of the bicycle study is

further confirmation that there are body actions which are

totally inaccessible to the consciousness. Both Lee and

Nashner in the experiments previously quoted found this

effect and it occurs as an aside in much of the postural

literature. None of the ten riders in the survey quoted in

chapter 3, nor any of the many other riders questioned by

the author have been able to describe correctly how they

exercised control, although almost all of them offered

explanations. The author, more aware than any of them of

the true direction of push during a turn, has never been

252


able to 'feel' that he was applying a torque against the

turn. The conviction that it is the rider who is causing

the rotation of the handle bars into the lean as the turn

develops, persists. In some strange contradictory way this

remains true even when the push is applied with a single

finger, which precludes the possibility of a pull.

Similarly no amount of mental effort has enabled him to

detect the operation of the basic balance loop on the

destabilized machine. These observations are a serious

warning against the reliability of introspective accounts

about how a skill is performed and goes some way to

explaining why many movement skills are taught so badly.

It is something of a paradox that riding a bicycle,

although very complicated, is comparatively easy to

investigate because the sys,tem is so constrained that it

allows only a limited range of possible control solutions.

It is likely that most of the other sports skills

mentioned in the previous section would be more difficult

both to record and simulate. However, since these skills

and many others, including skilled hand movements, are

likely to contain 'inaccessible sub-conscious' components

only a detailed record of the physical movements during

performance will reveal the secret of how the skill is

controlled.

253

Bicycle Riding References

References

Adams, J.A. (1971) A closed-loop theory of motor learning, Journal of Motor Behaviour, 3, 111-149

Adams, J.A. (1976). Issues for Motor Learning in Stelmach, G.E. trends, Academic Press, New York.

a Closed-Loop Theory of Motor Control issues and

Ballentine, R. (1983) Richard's Bicycle Book, Pan-Books, London.

Basmajian,J.V., Baeza,M. & Fabrigar, C. (1965) Conscious control and training of individual spinal motor neurons in normal human subjects, Journal of New Drugs 5, 78-85.

Bizzi, E. (19801 Central and peripheral mechanisms in motor control in Stelmach, G.E. & Requin, J. (eds) Tutorials in Motor Behaviour, Elsevier, North Holland.

Boylls, C. C. (1980) Cerebellar strategies for movement coordination in Stelmach, G.E. & Requin, J. (eds) Tutorials in Motor Behaviour, Elsevier, North Holland.

Boylls, C.C. & Greene, P.H. (1984) Signifi2ande Today in Whiting, H.T.A. (ed) Action, Elsevier, North Holland.

Bernstein's Human Motor

Cooke, J.D: (1980) The Organization of Simple, Skilled Movements ~n Stelmach, G.E. & Requin, J. (Eds) Tutorials in Motor Behaviour, Elsevier, North Holland.

Cordo, P.J. & Nashner, L.M. (1982) Properties of Postural Adjustments Associated with Rapid Arm Movements, Journal of Neurophysiology, Vol 47, No. 2, Feb.

Craik, control British

K.J.W. (1947) Theory of the human operator in systems, I, The Operator as an engineering system, Journal of Psychology, 38, 56-61

Davson.H & Segal.M.B, (1978) Introduction to Physiology; vol 4, Academic Press, London. Eaton, D.J. (1973) Man-machine dynamics in the stabilization of single track vehicles, Doctoral Thesis quoted in Weir & Zel1ner (1979).

254


Eldred, control Journal

E., Granit, R. & Merton, P.A. (1953) Supraspinal of the muscle spindles and its significance,

of Physiology, 122, 498-523.

Fernandez, C. & Goldberg, J .M. (1971) Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey, Journal of Neurophysiology, 34, I, I 635-660; 11 660-675.

Fernandez, C., Goldberg, J.M. & Abend, W.K. (1972) Response to static tilts of peripheral neurons ennervating otolith organs of the squirrel monkey, Journal of Neurophysiology, 35, 978-997

Gibson, J.J. (1950) The Perception of the Visual World, Houghton Mifflin, Boston.

Granit, R. (1970), The Basis of Motor Control, Academic Press, London & New York.

Grillner, S., Hongo, T. & Lund, S. (1969) Descending monosynaptic and reflex control of gamma-motoneurones, Acta physiologica Scandinavia, 75, 592-613.

Hallpike.C.S & Hood.J.D. (1953) Speed of the slow component of ocular nystagmus, Journal of the Proceedings of the Royal Society, 3, 216-230.

Healey, M. (1975) Principles of Automatic Control, Hodder and Stoughton, London.

Howard, I.P. & Templeton, W.B. (1966) Human Spatial Orientation, Wiley, London.

Jones, D.E.H. (1970) The Stability of the Bicycle, Physics Today, April, 34-40.

Keele; S.W. (1968) Movement control in skilled motor performance, Psychological Bulletin, 70, 387-402.

Keele, S.W. & Po~mer, M.I. feedback in rapid movements, Psychology, 77, 155-158.

(1968) Processing visual Journal of Experimental

Kelso, J.A.S., Holt, P.N., Kugler, P.N. & Turvey, M.T. (1980) On the Concept of Coordinative Structures as Dissipative Structures: 11. in Stelmach, G.E. & Requin, J. (eds) Tutorials in Motor Behaviour, Elsevier, North HOlland.

255


Kugler, P.N., Kelso, J.A.S. & Turvey, M.T. (1980) On the concept of coordinative structures as dissipative structures in Stelmach, G.E. & Requiin, J. (eds) Tutorials in Motor Behaviour, Elsevier, North Holland.

Kugler, P.N., Kelso, J.A.S. & Turvey, M.T. (1982) On the Control & Co-ordination of Naturally Developing Systems in Kelso, J.A.S. & Clark, J.E. (eds) The Development of Movement Control & Co-ordination, Wiley, New York.

Lashley, K.S. (1917) The accuracy of movement in the absence of excitation from the moving organ, American Journal of Physiology, 43, 169-194.

Lashley, K.S. (1929) Brain mechanisms and intelligence, University of Chicago Press, USA.

Lee, D.N. (1974) Visual information during locomotion in McLeod, R. & Pick, H. (eds), Perception: Essays in Honor of J.J. Gibson, Cornell University Press, Ithaca, 1974.

Lee, D.N., (1980) Visuo-motor coordination in space-time, in Stelmach, G.E. & Requin, J. (Eds), Tutorials in Motor Behavibur, Elsevier, North Holland.

Lee, D.N. & Aronson, E. control of standing in Psychophysics, Vol 15, No.

(1974) Visual human infants, 3, 529-532.

proprioceptive Perception &

Lee, D.N. & Lishman, J.R. (1975) Vision- the most efficient source of proprioceptive information for balance control, Symposium international de posturographie, Paris, 23 sep, 83-94.

Lishman, J,R. & Lee, D.N. (1973) The autonomy of visual kinaesthe.sis, perceptibn, 2, 287-294.

Lowell, J. & McKell, H.D. (1981) The Stability of Bicycles, The American Journal of Physics, 50(12), Dec.

Lund, S. & Pompeiano, o. (1965) Descending pathways with monosynaptic action on motoneurones, Experientia, 21, 602-603.

McLeod, P. (1977) A dual task response modality effect: support for multiprocessor models of attention, Quarterly Journal of Experimental Psychology, 29, 651-667.

McRuer, D.T. & Klein, R.H. in Smiley, A., Reed, L. & Fraser, M. (1980) Changes in Driver Steering Control with Learning, Human Factors, 22(4), 401-415.

256


Marler, P., (1970), Journal of Comparative Pysiological Psychology, Monograph, 71, 1-25.

Marsden, C.D., Merton, P.A. & Morton, H.B. (1971) Servo action and stretch reflex in human muscle and its apparent dependence on peripheral sensation, Journal of Physiology, 216, 21-22.

Matthews, P.B.C. (1972) Mammalian Muscle Receptors and their Central Actions, Arnold, London.

Nagai, M. (1983) Analysis of rider and single-track vehicle system, Automatica, Vol 19, 6, 737-740

Nashner, L.M. (1976) Adapting Reflexes Controlling the Human Posture, Experimental Brain Research, 26, 59-72.

Partridge, L.D. & Kim, J. H. (1969) Dynamic Characteristics of Response in a Vestibulomotor Reflex, Journal of Neurophysiology, 32, 485-495.

Pew, R.W. (1966) Acquisition of hierarchical control over the temporal organization of a skill, Journal of Experimental psychology, 71, 704-711.

Pew, R.W. (1974) Levels of analysis in motor control, Brain Research, 71, 393-400.

Robinson, D.A. (1977) Vestibular and optokinetic symbiosis: an example of explaining by modelling, in Baker, R., & Berthoz, A. (eds) , Control of Gaze by Brain Stem Neurons, Elsevier, New York, 49-58.

Ross Ashby, W. (1952) Design for a Brain Chapman & Hall, London.

Schmidt, R.A. (1975) A schema theory of discrete motor skill learning, Psychological Review, 82, 225-260. Schmidt, R.A. (1976). The Schema as a Solution to Some Persistent Problems in Motor Learning Theory in Stelmach, G.E. (ed) Motor Control issues and trends, Academic Press, New York;

Schmidt, R.A. (1980) On the Theoretical Status of Time in Motor-Pr6gram Representations in Stelmach, G.E. & Requin, J. Tutorials in Motor Behaviour, Elsevier,North Holland.

Shaffer,L.H. (1980) Timing Stelmach,G.E. & Requin,J. Behaviour, North Holland.

257

and Sequence of Action in (Eds), Tutorials in Motor

Bicycle Riding

Smiley, A., Reed, L. & Fraser, M. Steering Control with Learning, 401-415.

References

(1980) Changes in Driver Human Factors, 22 (4) ,

Stelmach, G.E. (1980) Egocentric referents in human limb orientation in Stelmach, G.E. & Requin, J. (eds) Tutorials in Motor Behaviour, Elsevier, North Holland.

Thompson, R.F. (1975), Introduction to Physiological Psychology, Harper International, New York & London.

Van Lunteran, A. & Stassen, H.G. (1967) Investigations of the Characteristics of a Human Operator, International Symposium on Ergonomics in Machine Design, Paper 27, Prague.

de Vries, H.A. (1967), Physiology of exercise, Staples press, London.

Weir, D.H. & Zellner, J.W. (1979) Lateral-directional motorcycle dynamics & rider control, Society of Automotive Engineers, Paper 780304.

Welford, A.T. (1974) On sequencing of action, Brain Research, 71, 381-392.

Whiting, H.T.A. (1980) Dimensions of Control in Motor Learning in Stelmach, G.E. & Requin, J. (eds) Tutorials in Motor Behaviour, Elsevier, North Holland.

Wilson, D.M. (1961) The central control of flight in a locust, Journal Experimental Biology, 38, 471-490.

Zanone, P.G. & Hauert, C.A. (1987) For a cognitive conception of motor processes, Cahiers de Pyschologie Cognitive, 7, 109-129.

258

I


Deliberately left blank.

259

Bicycle Riding Appendices

APPENDIX 1 (al

The Simulator programs

BIKEl The controlling program for the following two

routines. This sets up the parameters of the run and

initials the screen graphics.

AUTOSF The 'normal' bicycle control. This supplies the

basic front wheel stability and allows controlling pushes

to be introduced from the keyboard.

DESTAB The destablized control system. This feeds the

roll acceleration and velocity to the handlebar

acceleration at the set lag and gain. It allows pushes to

be superimposed either through the key board or

automatically at a selected threshold of lean angle.

MOMENTS This program works out the moments of inertia for

a new bicycle and stores them in the data files, BIKE_A,

BIKE B etc.

260


APPENDIX 1 (b)

The Destabilized Bicycle

A scale drawing of the Triumph 20 bicycle used in the

experiments. The original front forks are shown with a

dotted line. The following features are shown:-

el & eh Effective length and height. To allow for the

low density of the wheels the total length used for the

moments of inertia is shorter than the overall length.

The point 'el' lies approximately half-way between the 0.5

radius of gyration for a solid wheel and the 0.7 radius

for a wheel with all its mass at the periphery. Slightly

less has been subtracted from the vertical dimension.

~ The centre of mass (c of m) for the rider, assumed

constant. (Rider A 175 lbs, rider M 147 lbs).

b£l The c of m for the bicycle without the modification

to the front forks, (33 lbs) .

~ The c of m for the bicycle with the modification, (44

lbs) .

gg The c of m for the front fork additions (11 lbs).

~ The c of m for the combined system. The four crosses

show that the difference in rider weight and addition of

the front fork modification made very little change in the

location of the combined centre of mass.

272


APPENDIX 2 (a)

Angle Traces of the Destabilized Runs.

The roll and handlebar angle traces for twelve blindfolded

runs on the destabilized bicycle by two subjects. Runs 25

to 30 were by rider A and runs 31 to 36 by rider M. The

plots show the full run of 750 points. The horizontal

divisions show the recorded points which are at 30 msecs

intervals, thus the marked hundred intervals are

equivalent to 3 secs. The vertical scales have been

adjusted by multiplication during the graphing procedure

to bring the peaks as near together as possible to assist

a comparison between the rates of the two channels. This

conceals the large difference between their absolute

values and Table 5.1 on page 96 shows the maximum and

minimum lean and handle bar angles for each run taken from

the raw data files before conversion.

274


APPENDIX 2 (b)

Rates of Change of Angles for Destabilized Runs.

Limited sections (points 100-500) of the 12 destabilized

runs (25-36) are shown giving the roll and bar

relationship for angle, velocity acceleration and jerk.

See the text for full details. The bar channel throughout

is shown with a darker line than the roll channel. One

point in the horizontal scale is equal to 30 msecs. The

vertical scales have been adjusted to bring the peaks

together for easier comparison.

281


APPENDIX 2 (c)

Lag and Wave Dimensions for Destabilized Runs.

Histograms of lag, half-wave period and area measured on

the acceleration channel of the 12 destabilized runs

25-36. The two riders are shown separately. See text for

the method of extracting the matched waves. The letter

code at the start of each histogram identifies it as

follows:-

A or M Rider Identity.

D or N Destabilized or normal bicycle.

R or B Roll or Handlebar channel.

LAG Delay between roll & bar in data points (30

msecs) .

WAV Half-wave period length in data points (30

msecs) .

ARA Half-wave area in nominal units.

Thus ADRARA is rider A on the destab. bike roll areas.

294


APPENDIX 3 (a)

Effect of Gain on Stability.

The following four printouts from the computer simulation

of the destabilized bicycle under delayed roll/follow

control show the effect of changing gain on the stability

response. The intial disturbance is 2 degrees lean left

with a speed of 4 mph.

R

S

R' ,

S' ,

R'

Channel headings

Lean angle (roll)

Relative steering angle

Roll acceleration

Steering acceleration

Roll velocity

(degs)

(degs)

(degs/sec/sec)

(degs/sec/sec)

(degs/ sec)

The figures in brackets show the value of half the bar at the top of each vertical axis.

CRITICAL DAMPING The first graph shows a dead-beat response which is very nearly at the critical damping value for gain. Because the gain is low the response is slow and the lean angle is not contained till 10 degs.

STABLE OSCILLATORY The second graph shows the effect of increasing the gain from 90 to 200. The characteristic becomes oscillatory but the tendency is to converge and thus stable. The initial disturbance is contained by just over 3 degs in less than a second.

JUST STABLE The third graph shows that a further" small increase of gain to 220 puts the system into the 'just stable' condition where the oscillations neither converge nor diverge.

ONSTABI,E OSCILLATORY The fourth graph shows that increasing the gain beyond 220 puts the system into an unstable state where the oscillations diverge. Both the last two runs contain the initial disturbance by just over three degrees in less than a second.

300


APPENDIX 3 (b)

Regression Residuals for the Destabilized Runs.

The following graphs show the plots of those regression residuals predicting bar acceleration from roll acceleration and velocity which exceeded 1.96 of the standard deviation. The horizontal scale shows data points related to the original total run. The vertical scale has be adjusted to give a clear indication of location and the rate of change of value with time. Only the section 100 to 500 of the original run was used in each case. Each page contains two plots.

305

r


APPENDIX 3 (c)

Excess residuals related to the roll plots.

The following graphs show the location and direction of

the pushes implied by the excess regression residuals on

the plots of the roll angle for the runs 25-36, points

100-500. The arrows are located at the maximum value of

the excess residuals shown in the previous appendix and

show the direction in which the push tends to drive the

roll angle.

312

10 20 25 30 40 60 70 80

110 120 130 140 150 200 210 220 230 240 999

1000 1010 1020 1040 1080 1090 1500 1599 2000 2010 2020 2030 2050 2090 3000 3010 3020 3025 3026 3030 3040 3050 3060 3070 3075 3080 3090 3100

REM************************** REM BICYCLE CONTROL BIKEl REM**************************

REM This controls destabilised bike 6011T1 (Put in Temp for run) REM or autostab bike AUTOSF (Put in O.TEMP) Check line 240 graph=FALSE.@'l.=&00302 IF T1.(1 THEN PROCchoose ELSE T'l.=O:REM prevents calling itself DT$=" ".Fl=OPENIN"IDENT". INPUT£F1 ,DT$.CLOSE£Fl Ti=.01:NR=0:mm=304.8.CD=0 DIM CHC5,3),DIM D(5):NN=31:DIM NBCNN) F2=OPENIN"DIMS II :INPUT£F2,start,int:::CLOSE£F2:CH(1,1)=start CH(2,1)=CH(1,1)+int:CH(3,1)=CH(2,1)+int:CH(4,1)=CH(3,1)+int CH C5, U=CHC4, 1>+int " WB=O:Wradl=O:rake=O:trl=O:Mass=O:WT=O:HG=O:bar=O WIo=O.FIo=O:HIo=O:LIo=O:FwIo=O mph=O: VVy.=O: 5base=O:Vbase=O: 51=0: 52=0 Hl=0.H2=0.H3=0:H4=0:H5=O PF$="O.":FO$=PF$+"SIDE":REM Select auto (D.> or destab eN.)

REM********************************************* REM Main

mph=V'l./10:PROCspeedCmph):NR=R'l./I00 PROCnumbs_in(DT$):PROCallocate PROCsend_vals PROCti tl e C mph) CHAIN FO$

END REM***************************** DEF PROCsend_vals

F3=OPENOUT"VALS" PRINT£F3,Ti,Sl,S2,NR,CD,VV%,Mass,WB,HG,WT,Wlo,Flo PRINT£F3,Hlo,Llo,Fwlo,trl,Wradl,bar,rake CLOSE£F3

ENDPROC DEF PROCchoose:LOCAL DT$,FC,NR,mph.FC=50.CLS

REM Horizontal graph mUlt. facs. Width = 50/fac. H1=70.H2=170:H3=10:H4=25:H5=2 L'l.=C50/Hl)*100:M'l.=C50/H2)*100.N'l.=C50/H3)*100 07.=C50/H4)*100:PX=C50/H5) *100 REM REM Vert. graph mult. fac. 100 gives appx. B secs full screen Q'l.=150 PROCshow_facs(Hl,H2,H3,H4,H5,QZ) REM REM Names for channels. Refer to PRDCnames for code. A'l.=3:B'l.=2:C'l.=13.D'l.=15.E'l.=12 PROCshow_name(A%,B%,C%,OX,EX) REM

3105 3110 3130 3135 3140 3160 3170 3180 3190 3195 3196 3200 3210 3250 3300 3310 3320 3330 3399 6600 6620 6630 6650 7000 7010 7020 7030 7040 7090 8000 8010 8020 8090 8100 8110 8130 8140 8150 8160 8170 8175 8180 8185 8190 8300 8310 8320 8330

REM Source file for bike type DT$="BIKE_C II

REM REM Graph or Tables display_ Tables = -1, graph = 0 87.=0 REM REM Bike speed mph mph=6 REM ZY.=10:REM Lag in hundredths sec REM REM Initial ,lean error in degrees <positive left) NR=O PRDCbike_typeCDT$,mph,NR) PRINT TABC6,20); "If satis. hit RETURN." PRINT TAB(6,22);IIChanges in lines 3000,3999" INPUT A CLS:REM CHAIN"SCALES" ENDPRDC

DEF PROCnumbs_inCDT$):LOCAL M F4=OPENIN DT$:INPUT£F4,FT$

FDR M=l TO NN.INPUT£F4,NBCM):NEXT M:CLOSE£F4 ENDPROC DEF PROCallocate

Mass=NB(21):WB=NBC1):H8=NBC23):WT=NBC22):trl=NBC7) Wradl=NB(2):bar=NBC25)/2:rake=N8C6) WIo=NB(27):FIo=NB(28):HIo=N8C29):LIo=NBC30):FwIo=N8(31) CD=0.001417*WT

ENDPROC DEF PROCshow_facs(L,M,N,O,P,Q)

PRINT TAB(6,2);"Sizes of bars on graph axes" PRINT TAB(B,4);L;" ";M;" ";N;" 1';0;11 ";P

ENDPROC DEF PROCbike_typeCN$,mph,NR):LOCAL CH$,DR$

F5=OPENDUT" lDENT":PRINT£F5,DT$: CLOSE£F5 PRINT TAB(6,10);"Bike Type "DT$ IF 8Y.=0 THEN CH$="Graph" ELSE CH$=uTables" PRINT TAB C6, 12); "Display type "CH$ PRINT TAB(6,14);"Speed "mph" mph" IF S8NCNR)=O THEN DR$="right" ELSE DR$="left" PRINT TAB(6,16);lIlnitial error "NR" degrees "DR$ PRINT TAB(6,lB);"Gain ";J'l.;" Lag ";1'l. V7.=mph*10:R7.=NR*100

ENDPROC DEF PROCshow_nameCA,B,C,D,E):PROCnames

PRINT TABC6,6);"Channels selected" PRINT TABC8,8); PRINT name$(A);" ";name$(B);" ";name$(C);" ";name$(D);" ";name$(E)

8390 8400 8420 8425 8430 8440 8490 8500 8510 8520 8530 8550 8600 8605 8610 8620 8630 8640 8690 8700

ENDPROC DEF PROCspeedCmphl

VV~=INTCFN5peedCmphl+.SI

REM Next applies speed to gain factor. Sbase=220=Vbase=5:S1=Sbase*Vbase/(VV%*1000):S2=Sl*1.43 J%=Sbase

ENDPROC DEF PRDCtitleCmphl

PRINTIPRINT;TAB(3);DT$;1I IImph" mph"; IF OT$ <> "BIKE_Ell AND PF$ <> 110." THEN PRINT;" Gain IIJ'Y.," Lag "Z% IF DT$ ="BIKE E" THEN PRINT;" Riderless (Destab.)"

ENDPRDC .-DEF PRDCnames:LOCAL L~:DIM name$C201 REM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 DATA Secs,HA,RSA,VA,RA,Ll,L2,Fl,F2,FF,Hw,HwDOT,Vw,VwDOT,Sw,SDOT,Rw,SF,FFA

FOR L~=l TO 19 READ name$CL~1

NEXT ENDPROC DEF FNspeedCmphl:=CINTCCCmph*881/601*101/101

10 REM************************** 20 REM BICYCLE CONTROL AUTOSF 25 REM************************** 30 TF=O 35 VDU 23,240,24,48,96,255,255,96,48,24 36 VDU 23,241,24,12,6,255,255,6,12,24 40 DIM togg~(21.DIM opX(2I,DIM BU~(21'DIM Inc(2I,DIM SF(2I,DIM bias(21 50 DIM CH(5,3):DIM D(5)aDIM I(25):GF2X=~Xlmm=304.8:VV=0:lagX=ZX 60 DIM F(51.F(11=LX/100'F(2)=M~/100'F(31=N~/100'F(41=O'l./100,F(51=P'l./100

tOO-Ft=OPENIN"DIMS":INPUT£Fl,start,tnt:CLOSE£Fl:CH(t,l)=start 110 CHC2,1)=CH(1,1)+int:CHC3,1)=CHC2,1)+int:CHC4,1)=CH(3,1)+int:CH(5,1)=CH(4,1

)+int 120 Bu=O:AL=O:RSA=O 130 TS=O'g=32:R90=RAD(90) 140 Ld=O:RPY.=O;HL~O 150 F2=OPENIN"VALS":INPUT£F2,Ti,Sl,S2,NR,CD,VVX,Mass,WB,HG,WT,Wlo,Flo,Hlo,Llo,

Fwlo,trl,Wradt,bar,rake:CLOSE£F2 160 190 200 210 230 310 500 510 520 bOO 610 999

1000 1010 1030 1500 1530 1540 1550 1590 2499 2500 2590 2bOO 2620 2790 2959 3000 3010 3030 3050 3100

Ld-trl*mm:RPY.=Wradt*mm:HL=RADCrake) Preclo=Fwlo*2:Wldiam=Wradl*2:PC=Preclo*VVY.*PI*2/(Pl*Wldiam)

B1=O,B2=O,B3=O, B4=O,Cl=O, C2=O,C3=O'C4=O, C5=O, C6=0 HA=O, SA=O, VA=O: RA=O: Ll=O,L2=0:Fl=O:F2=0: FF=O: Hw=O, HwDO T=O,Vw=O,VwDOT=O Rw=O:SRw=O:WTg=0:FTg=O:SF=0:Trl=OISw=0:SPV1=O:SPV2=0:SPY3=O MOM=Mass*VVX:Si=VVX*Ti::REM Flo=Wlo;REM Both big Ffac=(VVXA1.8)*CD:T2=O.5*(TiA2):FIg=HG/Flo:WIg~HB/Wlo

LFlo=Llo+Flo:WBF=WB*Flo:HGL=HG*Llo:WGL=WBF/HGL WT1=WT/2=WB1=WB/2:WB2=(WBI A 2):CAC=Mass*(VVXA 2)IHlb=WBl/HIe

oprateX=FALSE: BU2h=O: cheqX=TRUE:NN%=O:prvRw=O bias=O:drn%=O::delyX=16:alac=.25:Inc=O::amp=0:Tm=0 REM********************************************* REM Main

graph=TRUE:TT=O VA=RAD(NR) REPEAT PROCrun

NN~=INKEY(l) UNTIL NNX=90 OR NN~=83 IF NNX=B3 THEN *PRINT

END REM*************************** DEF PROCcontrolCaccl)

SF=bias IF cheqX THEN IF NNX)O THEN PROCcheck IF oprateY. THEN PROCoprate(Inc,delyX)

ENDPROC REM***************************** DEF PROCcheck

IF NNX<65 THEN amp=FNamp(NNX) ELSE PROCturnCNN'l.,amp,delyX) NN7.=O

ENDPROC DEF PROCoprate(Inc,delyX)

3120 cheqX=FALSE 3130 bias=bias+lncISF=bias 3140 BU27.=BU2X+1 3150 IF BU27.=dely7. THEN BU2Y.=0.VDU5.MOVE 100,750,VDU 9,127.VDU4.cprate7.=FALS

E,cheqX=TRUE 3190 ENDPROC 3300 DEF FNamp(valX):LOCAL amp:amp=(val7.-4B)*a~ac:PROCshowit(amp):=amp 3400 DEF PROCturnCval'l.,amp,dely):LOCAL Nbias 3410 drnX=O 3420 IF valX=76 THEN drn1.=-l ELSE IF val'l.=82 THEN drnX=l 3430 Nbias=amp*drn;';lnc=FNinc(Nbias,bias,delyX) 3440 checkr.=FALSE:NNX~O:oprateY.=TRUE:PROCarrer 3490 ENDPROC 3500 DEF PROCshowit(val) 3520 VDU5:MOVE 100,aOO:VDU 9,9,9,9,127,127,127,127:PRINT val:VDU4 3550 ENDPROC 3555 DEF PRQCarrer 3560 VDU5,MOVE 100,750,PRINT"*".VDU 4 3570 VV7.=INT(TT*GF27.) 3575 IF val'i.=76 THEN XX;'=800:arr'l.=240 ELSE XX7.=SBO:arrY.=241 3580 VDU5,MOVE XX7.,VV7.,PRINT CHR$(arr7.).VDU4 3590 ENDPROC 3600 DEF FNinc(Nbias,bias,dely7.):=(Nbias-bias)/dely;' 3610 inc=(Nbias-bias)/dely'l.:PRINT inc*100:PRINT Nbias:PRINT bias;PRINT 4000 DEF FNforce(angle):LOCAL LL,sgn,val:sgn=SGN(angle):val=ABS(angle) 4010 IF angle~O THEN LL=O ELSE LL=(val*Ffac)*sgn 4020 =LL 4100 DEF FNhozdot(force):LOCAL I 4110 !=CHlo*COSCVA»+(Flo*SINCABS(VA»):=force*WB1/1 4200 DEF FNdlCvel,accl):=(vel*Ti)+(accl*T2) 4300 DEF FNvelCvel,accl):=vel+Caccl*Ti) 4400 DEF FNweight(VA),=WT*SIN(VA)*WIg 4500 DEF FNpetal(VA,FF).=FF*COS(ABS(VA»*FIg*-l 4600 DEF FNfwdotCSF,F1,VA,Tl,w,Sw) 4610 =C(PC*w)+CSF*bar)+(F1*Tl)+(WT1*SIN(VA)*Tl*-1»/Fwlo 4700 DEF FNturni Cforce):=ATN«force*Ti)/MOM) 4800 DEF FNhcirc(angle):=angle*WB1 4900 DEF FNturnw(angle):=angle/Ti 4999 REM************************************** 6000 DEF PROCrun:LOCAL HwDOT,VwOOT,Sdot,RAi,HAi,VAi,SAi,Roti,VSDOT,SSdot 6020 Fl=FNforce(OEG(Ll»:F2=FNforceCDEG(L2»:FF=F1+F2 6030 HwDOT=FNhozdot(F1-F2):VwOOT=FNweight(VA)+FNpetal(VA,FF) 6035 Sdot=FNfwdotCSF,Fl,VA,Trl,Vw,Sw) 6060 RAi=FNturni (FF):HAi=FNdl (Hw,HwDOT):VAi=FNdl (Vw,VwDOT): SAi=FNdl (Sw,Sdot) 6070 RA=RA+RAi:HA=HA+HAi:VA=VA+VAi:5A=5A+5Ai 6080 Roti=(FNhcirc(HAi)/Si):L2=HA-CRA-Roti):Ll=SA-(RA+Roti) 6090 Rw=FNturnw(RAi):Hw=FNvel (Hw,HwDOT):Vw=FNvel (Vw,VwDOT): Sw=FNvelCSw,Sdot) 6100 Trl =FNtrai 1 (RSA,VA):TT=TT+Ti 6120 B4=B3,B3=B2,B2=BI,BI=VwDOT

6125 6130 6135 6140 6190 6200 6999 7500 7510 7515 7520 7530 7590 7999 8200 8205 8206 8210 8230 8240 8260

C6=C5.C5=C4.C4=C3.C3=C2.C2=C1.C1=Sdot VSDDT= (Bl+B2+B3+B4)/4: PROCcontrol (VSDOT) SSdot=(Cl+C2+C3+C4)/4 RSA=SA-HA.SPV1=VwDOT.SPV2-VSDOT.SPV3-Sdot PROCdrafttDEB(VA) ,DEG(RSA) ,DEG(VSDOT) ,DEG(SSdot) ,DEB(Vw) ,TT)

ENDPROC REM******************* DEF PROCdraft(D(1),D(Z),D(3),D(4),D(S),TT)ILOCAL XXX,VYX:YVX=INT(TT*GF2X)

FOR M=l TO 5 XXX=(CH(M,l)-(D(M)*F(M») MOVE CH(H,2),CH(M,3):DRAW XXy.,VV'l.:CH(H,2)=XX;':CH(H,3)=VYX:NEXT IF INTITTI>TS THEN VDU 5.MOVE O,VVY..PRINT INTITTI,VDU 4.TS=TT

ENDPROC REM************************* DEF FNtrail (SA,VA):LOCAL b,SD,8W,CD,CH,Theta,6A,CA:SNX=O

SNY.=SGNIVA)*SGNISAI.SA=ABSISA).VA=ABSIVA)*SNY. IF SA=O THEN SA=.OOOOl SD=ATNITANISAI*SINIHLI).CD=COSISDI.CH=COSIHLI.SW=ACSICD*CHI b=RPY.*COSIACSIICH-ICD*COSISWI)I/ISINISDI*SINISWIIII Theta=(R90+(VA+SD»:GA=ATN( b/(RPX*-l*TAN(Theta») CA=GA-SW:=«RP%*SIN(CA»+Ld)/mm

•

10 REM************************** 20 REM BICYCLE CONTROL DESTAB 25 REM************************** 30 TF=O 35 VDU 23,240,24,48,96,255,255,96,48,24 36 VDU 23,241,24,12,6,255,255,6,12,24 40 DIM toggZ(2).D1M epX(2).D1M BUX(2),D1M 1nc(2).DIM SF(2).D1M bias(2) 50 DIM CH(5,3),D1M D(5),D1M I (25).GF2X=QX.mm=304.B.VV=0.lagZ=ZZ 60 DIM F(5).F(1)=LX/100.F(2)=MZ/100.F(3)=NY./100.F(4)=OZ/100.F (5)=P7./100 70

100 F1=OPENIN"DIMS": INPUT£Fl, start ,int: CLOSE£F1: CH (1,1) =start 110 CH(2,1)=CH(1,1)+int:CH(3,1)=CH(2,1)+int:CH(4,1)=CH(3,1)+int:CH(S,1)=CH(4,1

)+int 120 Bu=O:AL=O;RSA=O:gate=FALSE 130 Drcll=O;Orcll=0:Dturn=0:roll=0:TS=0:g=32:R90=RAD(90) 140 Ld=O'RPX=O.HL=O 150 F2=OPENIN"VALS":INPUT£F2,Ti,S1,S2,NR,CD,VV'I.,Mass,WB,HG,WT,Wlo,Flo,HIo,Llo,

Fwlo,trl,Wradl,bar,rake:CLOSE£F2 160 Ld=trl*mm: RPY.=Wrad1*mm: HL=RAD (rake) 190 Preclo=Fwlo*2:Wldiam=Wrad1*2:PC=Preclo*VV'l.*PI*2/(PI*Wldiam> 200 B1=0'B2=0.B3=0.B4=0'C1=0.C2=0.C3=0.C4=0.C5=0.C6=0 210 HA=0.SA=0.VA=0.RA=0.L1=0.L2=0.F1=0.F2=0.FF=0.Hw=0.HwDOT=O.Vw=O.VwDOT=O 230 Rw=O:5Rw=0;WTg=0:FTg=0:5F=0:Trl=0;Sw=0;SPV1=0;SPV2=0;SPV3=0 310 MOM=Mass*VV'l.:Si=VV'l.*Ti::REM Flo=WIo:REM Both big 500 Ffac=(VV'!.Al.8)*CD:T2=O.5*(TiA2):FIg=HG/FloIWIg~HG/Wlo 510 LFlo-LIo+Flo:WBF=WB*Flo:HGL=HG*Llo:WGL=WBF/HGL 520 WTl=WT/2.WBl=WB/2.WB2=(WB1 A 2).CAC=Ma55*(VVZA 2).Hlb=WBlIH1e 600 oprateh=FALSE:togg'l.(1)=TRUE:togg'l.(2)=TRUE:NN'l.=0:prvRw=0 610 drn'l.=0:Odrn'!.=O:delyX=30:amp=0:afac=.005:wayh=O:Tm=0 999 REM*********************************************

1000 REM Main 1010 graph=TRUE.TT=O 1030 VA=RAD(NR) 1500 REPEAT PROCrun 1530 NNY.=INKEY(l) 1540 UNTIL NNZ=90 OR NNX=B3 1550 IF NNX=B3 THEN *PR1NT 1590 END 2499 REM*************************** 2500 DEF PROCcontrol(accl,velo):LOCAL acfac,velfac 2550 acfac=(accl*Sl):velfac=(velo*S2) 2560 1(25)=1(24).1(24)=1(23):1(23)=1(22).1(22)=1(21).1(21)=1(20).1(20)=1 (19) 2565 I (19)~1 (1B).1 (1B)=1 (17).1 (17)=1 (16). I (16)=1 (15).1 (15)=1 (14). I (14)=1 (13) 2570 1(13)=1 (12). I (12)=1 (11).1 (11)=1 (10).1 (10)=1 (9): I (9)=1 (8). I (B)=I (7) 2575 1(7)=1(61.1(6)=1(5).1(5)=1(4).1(4)=1(3) 2580 I(3)=I(2):1(2)=1(1):1(1)=acfac+velfac:REM +(VA/l0) 2590 REM GOTO 2620 2610 IF Tm>O THEN Tm=Tm-l ELSE PROCthresh 2620 IF togg'l.(l) THEN IF NN'l.>O THEN PROCcheck

2640 2680 2700 2790 2959 3000 3010 3030 3050 3100 3120 3130 3140 3145 3150 3190 3200 3210 3220 3250 3300 3310 3320 3400 3420 3430 3440 3450 3460 3465 3470 3490 3500 3510 3590 3600 3610 3620 3690 3850 4000 4010 4020 4100 4110 4200 4300 4400

IF op%(l) THEN PROCoprate(dely%~l) REM IF cp'l.(l) THEN SF=SF(I) ELSE SF=I(lag'l.)

SF=I(lagX)+5F(1) ENDPROC REM***************************** DEF PROCcheck

IF NN'X<76 THEN a·mp=FNarnpCNNX) ELSE PROCturnCNN1.,amp,delyX,l) NN'l.=O

ENDPROC DEF PROCcprate(delyX,tpX)

tcgg'l. (tp'l.) =FALSE biasCtpX)=biasCtpX)+IncCtpX):SFCtp'l.)=biasCtp'l.) BU'l.(tp'l.)=BU'l.(tp'l.)+1 IF BUYo(tp'l.)=(dely'l./2) THEN Inc(tp'l.)=Inc(tp'l.)*-1 IF BU'l.(tpX)=delyX THEN PROCbucket

ENDPROC DEF PROCbUcket

BU'l. (tpYo) =0: cp'l. (tp'l.) =FALSE, tcggYo (tp'l.) =TRUE VDU5:MOVE lOO,750:VDU 9,127:VDU4

ENDPROC DEF FNampCval'l.):LOCAL amp:amp=(val7.-48} PROCshowitCamp) =amp*afac DEF PROCturn(val'l.,amp,dely'l.,tp'l.):LOCAL Nbias,way'l.,arrY.

IF val'l.=76 THEN way7.=-l ELSE IF val'l.=82 THEN wayY.=l Nbias=amp*way'l.:lnc(l)=FNincCNbias,dely'l.) tcgg'l.(tp'l.) =FALSE: NN'l.=O:opYo (1)=TRUE VDU5:MOVE lOO,750:PRINT"*":VDU 4 YY'l.=INT(TT*GF2Y.) IF val%=76 THEN XXX=800Iarr%=240 ELSE XXY.=5BO;arr'l.=241 VDU5:MOVE XX7.,YV%:PRINT CHR$(arrX):VDU4

ENDPROC DEF PROCthresh;LOCAL roll,pokeX:pokeX=16

roll=DEG(VA);IF ABS(roll»1.6 THEN PROCpulse(pokeY.,SGN(roll» ENDPROC DEF PROCpulse(val,drnY.)

IF drnY.=-1 THEN NNYo=76 ELSE IF drnX~1 THEN NNX=82 amp=FNamp(val+4S):Tm=100

ENDPROC DEF FNinc(Nbias,delyY.):=(Nbias)/{delyY./2) DEF FNforce(angle):LOCAL LL,sgn,val:sgn=5GN(angle):val=ABS(angle)

IF angle=O THEN LL=O ELSE LL=tval*Ffac)*sgn =LL DEF FNhozdot(force):LOCAL I

I=(Hlo*CDS(VA»+(Flo*SIN(ABS(VA»):=force*WB1/1 DEF FNdl (vel ,accl):=(vel*Ti)+(accl*T2) DEF FNvel (vel,accl):=vel+(accl*Tl) DEF FNweight(VA):=WT*SIN(VA>*Wlg

4500 4600 46io 4700 4800 4900 4999 6000 6020 6030 6035 6060 6070 6080 6090 6100 6120 6125 6130 6135 6140 6190 6200 6999 7500 7510 7515 7520 7530 7590 7999 8500 8520 8590 8600 8700 8710 8720

DEF FNpetal(VA,FF):=FF*COS(ABS(VA»*FIg*-l DEF FNfwdct(5F)

=«SF*bar»/Fwlo DEF FNturni(force):=ATN«force*Ti)/MOM) DEF FNhcirc(angle):=angle*WBl DEF FNturnw(angle)~=angle/Ti REM************************************** DEF PROCrun:LQCAL HwDOT,VwDOT,Sdot,RAi,HAi,VAi,SAi,Roti,VSDOT,SSdot

Fl=FNforce(OEG(Ll»:F2=FNforce(DEG(L2»:FF=Fl+F2 HwDOT=FNhozdot(Fl-F2):VwDOT=FNweight(VA)+FNpatal(VA,FF) Sdot=FNfwdot(SF) RAi=FNturni (FF):HAi=FNdl (Hw,HwDOT):VAi=FNdl (Vw,VwDOT):SAi=FNdl (Sw,Sdot) RA=RA+RAi1HA=HA+HAi:VA=VA+VAi:SA~SA+SAi

Roti=(FNhcirc(HAi)/Sj):L2=HA-(RA-Roti):L!=SA-(RA+Roti) Rw=FNturnw(RAi):Hw=FNvel (Hw,HwDOT);Vw=FNvel (Vw,VwDOT): Sw=FNvel{Sw,Sdot) TT=TT+Ti:REMTrl=FNtrail(RSA,VA) B4=B3.B3=B2.B2=Bl.Bl=VwDOT C6=C5.C5=C4.C4=C3.C3=C2.C2=Cl.Cl=5dct VSDOT= (Bl+B2+B3+B4)/4: PROCcontrol (VwOOT,Vw) SSdot=(Cl+C2+C3+C4)/4 R5A=5A-HA,5PV1=VwDOT.5PV2=V5DOT.5PV3=5dct PROCdraft{OEB(VA) ,DEB(RSA),DEB(VSDOT) ,DEB(5Sdot),DEG(Vw) ,TT)

ENDPROC REM******************* DEF PROCdra4t(D(1),D(2),D(3),D(4),O(S),TT):LOCAL XX%,VY%:YV%=INT(TT*GF2'l.)

FOR M=l TO 5 XX'l.=(CH(M,l)-(D(M)*F(M») MOVE CH(M,2),CH(M,3):DRAW XXX,VV1.:CH(M,2)=XXX:CH(M,3)=YVX:NEXT IF INT(TT»T5 THEN VDU 5.MOVE O,VV'l..PRINT INT(TT).VDU 4.TS=TT

ENDPROC REM************************* DEF PROCtitle PRINT;TAB (3) ; OT:$; "Speed= "FNmph (VV'l.)" mph . Sl "51" 52 "92 ENDPROC DEF FNmph(fps)1=(fps/SB)*60 DEF PROCshowit(val)

VOU5:MOVE lOO,BOO:VDU 9,9,127,127:PRINT val:VDU4 ENDPROC

10 REM************************************* 20 REM FINDING MOMENTS OF INERTIA ~O REM************************************* 50 NN=26.N2=5.DIM NM$(NN).DIM NB(NN).DIM DM$(NN).DIM DT$(NZ).DIM DT(N2) 90 @X=&20309:satis=0:DT$=II"

100 WB=O: Wradl=O: Wrad2=0: bi' kea=O:bi keb=O:rake=O' trl=OI Bmas=O: FWma9=O 110 Sgravl=0IBgrav3=0~Sgrav2=0=Bgrav4=0:Mht=0:Mrad=0:Mma9=O:Mgravl=O 120 Mgrav3=0: Mgrav2=O:Mgrav4=0: mass=O:WT=O:HG=O,LG-O:bar=O :barmas=O 136 Fwfac=I.4144:REM Convert to solid disc equivalent 150 WIo=O:REM Vert moments about Ground contact point 160 Flo=O:REM Vert moments about C of G 170 Hlo=O:REM Hoz moments about C of G 180 Llo=O:REM Hoz moments about rear wheel 190 g=32:REM Gravity 199 REM********************************************* 200 REM Main 210 CLS 220 PROCnames:PROCnumbs_in:PROCallocate 600 PROCmoments:DT(5)=FNfwheel(Wradl,Fwfac,FWmas,bar,barmas):REM Fwlo 800 PROCfinal:PROCshow:IF satis THEN PROCfile 900 MODE 3.END 999 REM********************************************:::

1000 DEF PROCmoments 1010 LOCAL Hmom,Bmom 1040 REM Vert ----------------------1050 Mmom=Hmas*«{Mrad~2)/4)+«Mht~2)/12»:Bmom=Bmas*Cbikea~2)/12 1055 REM about road contact pt. 1070 DT(I)=FNmoms(Mgravl,Bgravl):REM Wlo 1080 REM Vert about CG 1090 DT(2)=FNmomsCMgrav2,Bgrav2):REM FIe 1100 REM Hoz -----------------------1110 Mmom=Mmas*CMrad~2)/2:Bmom=Bma5*(bikeb~2)/12 1115 REM about CB 1120 DT(3)=FNmomsCMgrav4,Bgrav4):REM HIe 1125 REM about rear wheel 1130 DT(4)=FNmoms(Mgrav3,Bgrav3):REM LIo 1140 ENDPROC 1150 DEF FNmomsCman,bike):=(Mmom+(Mmas*(manA 2»)+CBmom+(Bmas*(bikeA 2») 1200 DEF FNfwheel(rad,fac,Wmas,bar,barmas):LOCAL Qrad,Wmom,Bmom 1210 Bmom=barmas*Cbar~2)/12 1220 Qrad=rad*fac:Wmom=(Wmas*(Qrad~2)/4)

1230 =Wmom+Bmom 2000 DEF PROCnames 2010 DATA "Wheel Base" ,"Front Wheel RadII, "Rear Wheel Rad tl , "Effect. Ht" 2020 DATA "Effect. Lgth", "rake", tltrl" ,IIBi ke mass", "FWmass", "Bgravl", "Bgrav3", tls

grav2", "Bgrav4" 2030 DATA "Man Ht", "Man Rad", "Man Mass", "Mgrav1", "Mgrav3", "Mgrav2", "Hgrav4" 2040 DATA "Comb Mass", "Comb WT", "Comb Grav Ht", "Comb Grav Lgth 11 ,"Bar eff. I ngth"

1 "Bar mass" 2050 DATA "ft", "ft" I "ft", "ft", "ft·" "degs", "ft", "slugs", "slugs", "ft", "ft", "ft"

2060 2070 2090 2095 2100 2150 3000 3010 3090 3500 3510 3520 3530 3590 6100 6200 6300 6500 6510 6520 6530 6540 6560 6590 6600 6620 6630 6690 7000 7010 7020 7030 7040 7050 7090

DATA "ft", "ft", "ft", "slugs", "ft", "ft" I "ft", "ft" DATA "slugs","lbs","ftll,"ft","ftll,"slugs" DATA "Vert about rDada WIo", "Vert abDut CG. FIe", "Hoz. about CB. HIe" DATA "Hoz.. about rear wheel. LIo", "Front wheel Assy. Fwlo" PROCnames_in:PROCdims_in:PROCans_in ENDPRDC DEF PROCflnal'LOCAL M

PRINT TAB(0.5).FOR M=1 TO N2.PRINT TAB(40); DT$(M);TAB(70);DT(M).NEXT ENDPROC DEF PROCfl1e.LDCAL M

F2=OPENDUT "NEWBIK".PRINT£F2.DT$ FOR M=1 TO NN.PRINT£F2.NB(M).NEXT M FOR M=1 TO N2.PRINT£F2.DT(M).NEXT M.CLOSE£F2

ENDPROC DEF PROCnames_in:FOR M=l TO NN:READ NM$(M):NEXT M:ENDPROC DEF PROCdims_in.FOR M=l TO NN.READ DM$(M).NEXT M.ENDPROC DEF PROCans_in:FOR H=l TO N2:READ DT$(M):NEXT M:ENDPRQC OEF PROCshow

PRINT TAB (43,1) ; "Moments of Inerti a for "DT$ PRINT TAB(43,2);"----------------------------":PRINT TABe 0,0) FOR M=1 TO NN:PRINT NM$(M);TAB(17);NB(M);TAB(27);DM$(M).NEXT PRINT TAB(40,15);"ls this OK to file? y/n II p YS=GET$ IF Y$="Y" OR V$="y" THEN satis=l ELSE satis=O

ENDPROC DEF PRDCnumbs_in:LOCAL M

Fl=OPENIN "TRANS".INPUT£Fl.DH FOR M=1 TO NN:INPUT£Fl.NB(M).NEXT M.CLOSE£Fl

ENDPROC DEF PRDCallocate: WB=N8(1):Wradl=NBC2):Wrad2=NB{3)

bikea=NB(4):bikeb=NB(5):rake=RADCNB(6»:trl=NB(7):Bmas=NBCS) FWmas=NB(9):Bgravl=NB(10):Bgrav3=N8(11):Bgrav2=NBC12):Bgrav4=NB(13) Hht=NB(14):Hrad=N8(15):Hmas=NB(16):Hgravl=NBC17):Mgrav3=NB(18) Mgrav2=NB(19):Hgrav4=NB(20):mass=NB(21):WT=NB(22):HG=NB(23):LG=NB(24) bar=NB(25):barmas=NB(26)

ENDPROC

--o

--- ---- --- --- --- ----- -- -- +-+ ----+ _--++~-----3

, \ \

-....... --~ ............. (")

----- ,,.. (,Q ............. \,1I0oI

~I , 'f." f~,,\AY . .l

'.'

E ent

I 11 1111111111 I 1111 I11 11 I 11 I 11 11 11 I t 11 I 11111 I I 11 1111 I11 11 11 1111 I11 I11 111111 I

188 288 388 488 588 688 788

Run 25. Roll and Ba~ angles

E ent

I i I11 i i i I i I i i 11111 i 11 i 111111111111 i 11111111 i I i I ill i 1111111111111111111 i i 11 i

188 288 308 488 588 688 788


. .,.., ~'-'.' ~I~

E ent

? ?

""""'1""""'1""""'1""""'1""""'1""""'1""""'1"'" 180 288 300 400 500 600 780

Run 27. Roll and Bar angles

(.1 I, I ... 1 11;,;.i1't _.~r 9 ....... ;:J ...... ,

'u' .'} 1:::....1 ............. ,1 ....

'-,

E ent

I, , , , , 11 , 'I' ill' 11 , 'I' , , , , , , , , ! ' , , , , , , , 'I' , , , , , , iI i ' , 11 , , , , i 1"11 , 1 i , 1 111 , , 1

180 288 388 408 588 608 708


E ent

11111111111111111111111111111111111111111111111111111111111111111111 1111111

100 200 388 488 588 688 788


\.--~:..[

E ent

1111111111111 i I i 1111111111 i 111111111 i I i i 11 i I11 i 11 i I11 I11 Ill! 111111111 i 11111

188 288 388 488 500 6eS 7S0


E ent

1111111111111111111111111111111111 1111111 1111 I Ill! 1111111111111111111111111

~ee 2ee 3ee 4ee see 6e0 700


Efent

I11111111 i j I i i i 111111111 i i i 11 i 111111 i I i 11 i i i i i i i I i 111111 i I i i j i 11111 i 1111 i i 11

I ~0e 200 300 400 509 699 790


E en-t

? ?

111111111111111111111111111 111111111111 111111111111111111111111111111111111

100 200 300 400 500 600 700

·Run 33·, Roll and Bar angles

..... I!') !-.

I'I:~} \'. 1t.!{J~ '.

E ent

1'1 j IIIII i 11 i i I i 1\ i i I i i i i 11 i III1 '111.11 i Illllill i I i i I' i 111\ i i '1111111111111 i I i

I 10a 209 3a0 4a0 500 6a8 708


- A l·~ .J't.... - ,."j'l.J c. .' I '<-.. ,.,.,. .'1'/ L I ,'): till f I I'

. '':.no ,/"'-')',,.. I 1 •. :;. ........ ;rh I I ~d.~'~ 11 ~ ! IIL..-----+f--' I ~. i ~ _.t ~ ~ .... I I,. j r'l J .. I 1.1... I' I, l ......... ,_ ", -. ,--,' -"'''''''-', ,I' Id} t .. /,' ---..O"\;f .... .....,. ~ .~ .. I".,l' \Lr~l

I,' '- ......., r,l ~ ..... .I·L'11 ' ... '..... ~-.......J. '.1

E ent

111111111111111111111111111111111111111111111111111111111111111111111111111

109 209 308 408 500 600 700


E ent

11111111111111111111111111111111111111111111111111111111111111111111 1111111

188 208 388 488 588 688 788


Run Ho 25 Roll and 8ar (dal'k line) 8n91e ?

1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 1 1 1 -I 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 288 389 498 588

Run Ho 25 Roll and 8ar (dark line> Velooity

1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 288 388 488 588

Run Ho 25 Roll and Oar (dark line) 800ln ?

1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 288 388 488 588

Run Ho 25 Roll and Bar (dark line) Jerk ?

11 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1- 1 1 1 I 1 1 1 1 1 1 1 1 1 I 218 388 481 511

? Run Ho 26 Roll and Bar (dark lin.) Angle

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 218 al8 41. 58.

? Run Ho 26 Roll and Oar (dark line) Velooity

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 2B8 a88 4BB 58.

Run Ho 26 Roll and Oar (dark line) ftccln ?

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 2BB a88 48B 5BB

Run Ho 26 Roll and Oar (dark line) Jerk ?

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 2BB 388 488 588

Run Ho 27 Roll and Bar (dark lino> nnglo

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 288 388 488 588

Run Ho 27 Roll and Bar (dark lino> Uoloeity


Run Ho 27 Roll and Bar (dark lino> Reeln

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 288 398 488 588

Run Ho 27 Roll and Bar (dark lino> lerk

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 288 398 488 588

? Run Ho 28 Roll and Bar (dark line) Angle


? Run Ho 28 Roll and Bar (dark line) Uelocity


Run Ho 28 Roll and Bar (dark line) Accln ?

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 28B 388 488 588

Run Ho 28 Roll and Bar (dark line) Jerk ?

i I I I I I I I I I I I I I I I I I I I I I I I I 288 388 488 588

? Run Ho 29 Roll and Bar (dark line> Angle


? Run Ho 29 Roll and Bar (dark line> Uelocity


Run Ho 29 Roll and Bar (dark line> Rccln ?


Run Ho 29 Roll and Bar (dark line> 1erk ?


· - -.', .. , ~- ..

Run Ho 31 Roll and Bar (dark lin~) Hngl~

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 21. 3.1 4.1 511

Run Ho 3. Roll and Bar (dark line) Uelocity

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 2.1 31. 41. 511

Run Ho 38 Roll and Bar (dark line) Hccln ?


Run Ho 3. Roll and Bar (dark line) Jerk ?


Run Ho 31 Roll and Bar (dark line> flngle

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 288 388 488

Run Mo 31 Roll and Bar (dark line> Velocity


Run Ho 31 Roll and Bar (dark line> flccln

v


Run Ho 31 Roll and Bar (dark line> Jerk

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 2B8 388 488 588

Run Ho 32 Roll and Oar (dark line> Rngle 1


Run Ho 32 Roll and Oar (dark line> Ueloeity


Run Ho 32 Roll and Oar (dark line> Reeln

R •

~~~#J!~ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

289 388 488 588

Run Ho 32 Roll and Bar (dark line> Jerk

I I I I I I I I I I I I I I I I I I I I I I I I

289 388 488 588

, ',._'. . '- ,.'-.

?

?

?

?

- .. '~ ~'- .

Run Ho 33 Roll and Oar (dark linp) 8ng\p

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

288 388 488

Run Ho 33 Roll and Oar (dark line) Velocity

1111111111

588


Run Ho 33 Roll and Oar (dark line) Rccln

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 288 388 488

Run Ho 33 Roll and Oar (dark line) Jprk

111111111

588

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I· I I I I I I I I I I 288 388 488 588

Run Ho 34 Roll and Oar (dark lin!) Rngl! ?


? Run Ho 34 Roll and Bar (dark line) Ueloeity


Run Ho 34 Roll and Bar (dark line) Reeln ?


Run Ho 34 Roll and Oar (dark line) Jerk

I I I I I I I I I r I I I I I I I I I I I I I I I I I I I I I I I I I I 288 388 488 588

? Run Ho 35 Roll and Oar (dark line) Rngle


1 Run Ho 35 Roll and Oar (dark line) Velocity


Run Ho 35 Roll and Oar (dark line) Rccln 1


Run Ho 35 Roll and Oar (dark line) Jerk ?

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

288 388 488 588

? Run Ho 36 8011 and Oar (dark line) 8ngle


Run Ho 36 Roll and Bar (dark line) Velocity

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 288 388 488 588

Run Ho 36 8011 and Ba,' (da,'k line) Rccln

288 388 488 588

and Bar (dark line) Jerk ?

f I

I

l J I I I I I I I I I I I I I I I I I I I 1111111 I I I I I I I I I I I I I

288 388 488 5~8

t1DRARA all runs

Mid-pt Freq

5 13 ************* 15 10 ********** 25 20 ******************** 35 16 **************** 45 18 ****************** 55 14 ************** 65 20 ******************** 75 10 ********** 85 18 ****************** 95 13 ************* 105 16 **************** 115 12 ************ , 125 8 ******** 135 9 ********* 145 10 ********** 155 14 ************** 165 9 ********* 175 6 ****** 185 6 ****** 195 9 *********

* (1) Mean = 114.114094

MDBARA all runs

Mid-pt Freq

5 17 15 13 25 24 35 17 45 18 55 15 65 16 75 17 85 18 95 24 105 9 115 13 125 18 135 6 145 11 155 8 165 8 175 10 185 3 195 0

* Cl)

***************** ************* ************************ ***************** ****************** *************** ***********'***** ***************** ****************** ************************ ********* ************* ****************** ****** *********** ******** ******** ********** ***

Mean 100.422819

Std. Dev.= 83.7320775

Std. Dev.= 81.6115518

ADRARA all runs

Mid-pt Freq

5 19 15 12 25 5 35 14 45 12 55 8 65 12 75 7 85 11 95 12 105 12 115 8 125 15 135 12 145 6 155 7 165 9 175 7 185 7 195 7

* (1)

******************* ************ ***** ************** ************ ******** ************ ******* *********** ************ ************ ******** *************** ************ ****** ******* ********* ******* ******* *******

Mean 115.298755 Std_ Dev.= 79_2304923

ADBARA all runs

Mid-pt Freq

5 28 15 16 25 5 35 8 45 9 55 12 65 12 75 14 85 12 95 11 105 5 115 7 125 15 135 7 145 7 155 3 165 5 175 7 185 8 195 10

* = (1)

**************************** **************** ***** ******** ********* ************ ************ ************** ************ *********** ***** ******* *************** ******* *******

*** ***** ******* ******** **********

Mean 116.091286 std. Dev.= 104_80264

f'1DRWAV all runs

Mid-pt Freq

1 0 3 5 5 13 7 46 9 68 11 61 13 33 15 21 17 15 19 14 21 8 23 8 25 2 27 2 29 2 31 0 33 0 35 0 37 0 39 0

* (2)

** ****** *********************** ********************************** ****************************** **************** ********** ******* ******* **** ****

* * *

Mean 11.2013423 Std. Dev.= 4.83760419

MDBl-'JAV all runs

Mid-pt Freq

1 3 3 5 5 10 7 48 9 85 11 58 13 33 15 23 17 11 19 6 21 6 23 3 25 2 27 4 29 1 31 0 33 0 35 0 37 0 39 0

* (2)

* ** ***** ************************ ****************************************** ***************************** **************** *********** ***** *** *** * * ** ..

Mean 10.4261745 Std. Dev.= 4.52690534

ADRl'JAV all runs

Mid-pt Freq

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

o 2 14 16 21 29 44 30 33 24 6 6 6 2 3 4 1 o o o

( I )

ADBWAV all runs

Mid-pt Freq

I 4 3 8 5 21 7 20 9 26 11 35 13 41 15 29 17 15 19 19 21 12 23 6 25 4 27 0 29 0 31 1 33 0 35 0 37 0 39 0

* (1)

** ************** **************** ********************* ***************************** ******************************************** ****************************** ********************************* ************************ ****** ****** ******

** *** **** *

Mean 13.8381743 Std. Dev.= 5.72201427

**** ******** ********************* ******************** ************************** *********************************** ***************************************** ***************************** *************** ******************* ************ ****** ****

Mean 11.9917012 Std. Dev.= 5.47570394

ADU::'G all runs

Mid-pt Freq

0 0 1 28 2 27 3 49 4 43 5 37 6 16 7 18 8 12 9 6 10 2 11 1 12 2 13 0 14 0 15 0 16 0 17 0 18 0 19 0

" = (2)

************** ************* ************************ ********************* ****************** ******** ********* ******

*"" * .. *

Mean 4.2033195 Std. Dev.= 2.28020286

MDLAG all runs

Mid-pt Freq

0 0 1 19 2 75 3 88 4 62 5 35 6 7 7 1 8 4 9 4 10 2 11 1 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0

" (2)

********* ************************************* ******************************************** ******************************* ***************** .... * " ** "* * ..

Mean 3.36912752 std. Dev.= 1.63579504

5 \ 1

4 I \

3

\ 2

.1. \ \

\

..... ph Gain S

90 Lag .1.2

( 5) (.1.0) (.1.0)

\ ) \\ /

... r/O ./

( ( ---

I

I

./

("

BIKE C 4 Mph Gain 288 Lag 12 Secs R S R~~ S~~

( 2) ( 2) (18) (15)

? ( ,(

5 --" ;,) )

4 ( ( < ) ->

(~~~ ( ( 3 ---.

-) ~.

,------ ----~

2 ( ) c:- ------- ---• --~

'i" ---") _____ ... 1

--- --(

---\ <~~- '-

( -----

1 f-~~-::::;, _---

------., -

\ --- c-----1-----

<. -----

R~

5) (

)

( }

(

D (

t'l , (

BIKE C 4 Secs R

( 2)

5

4

3

2

1

l\

..... ph

S (

"'-, ./

C) ('

) (

)

:> '" ..... , ..

Gain 228 Lag 12 S~~

2) (25)

--

<--=-~-=~ r-------- ( (.:----

~~~~~::;, ) --- -------::. ~-- ---- ( ·C: (:----r---... ) ~-==--~-, ,------ '-----;>

r----- ------ ( "-----

1------;. --=--=-.-=.-".) )

---- --- r;:----- ( .:: -----~--1------ -----....

.. , __ ---..I " )

( ,------r------ [:=~=~ ------

I---~ -----) 1'-, .) -----

...

,---- 1---- (----- ( --

3

2

J_

/"

~ ')

( \

Mph Gain 248 Lag 12 S R........ S ........ R~

( 2) (28) (55) ( 5)

---- 1-- ---:::~.> _.:=:-:.. ---1----- 1;---

<-::-=-_ , ------1--r--_ _-:.-::--"".::. ~,

----1-----r';:------

-~~~:~ (" ---

(-- (

Run 25 Residuals >1.96 std. dev ?

?

I I I I " I 11 I I I

280

I I I I I "l" 300

I I I I I "l" .400


?

I I I I I I I "1" 280

11 I I I "1" 300

I I 11 I I

11

I I I I

488

I I I I I I I I 501

.. ,-.-


1-

·'1

H 11

I I I I I I I I I I 11 11 I I

290

I I I I I I I I I I I I I I I I 409 '501

Run 28 Residuals >1.96 std. deu ?

1-

I

\ j (I -1' ~ ~ it

'I' ,

I I i I i 1 I I i i I , 400

I I I I '501

Run 29 Residuals >1.96 std. dev ~

1"

"

/

I I I I I I I I I 1 I I I I I I I 11 1 I I I I I I I

288 388

Run 38 Residuals >1.96 std. dev ~

1"

I I I I I I I I I 1 I I

288

I I I I I I I 1 I I

388

I I I I I I I 1 I I

488

I I I I I I I 1

581

11111111

581

Run 3~ Residuals >~.96 std. dev ? ?

I I 11 I I I I I I I I

288

I I I I I I I I I I

388

I I I I I I I I I I

488

Run 32 Residuals >~.96 std. dev ?

?

I I I I I I I I I I I I

288

I I I I I I I I

399

I I I I I I I I

499

I I I I I I I I 591


?

" I I I I I I I I I I "l" 399

I I I I I I I I " 499

I I I I I I I I 591

Run 34 Residuals >1.96 std. dev '~

1"

I I I I I I I "l" 299

I I i I I I

390

I I I

\,1 Il "

I I " " 499

Run 35 Residu~ls >1.96 std. deu ? 1-

1 1 1 1 1 1 1 1 1 I 1 i

288

1 1 1 1 1 1 1 I 1 1

388

IJ

1 1 1 1 1 1 1 I 1 1

488

Run 36 Residuals >1.96 std. deu ?

1-

i 1

1 1 1 1 1 1 1 I 581

~u-~------nr---·-----~~------------------·--,,-----'ll

1 1 1 1 1 1 1

IJ

"1" 280

1 1 1 1 1 1 1 i ill 1 1 I

388

11 1 I Ii 488

Run 25 Roll angles + pushes '?

.--" .'-',

--........ -.. -........ J.--_ ... -

, , , , 11 , "I" 288

11 , " , , 11 , "1""""'1 488 581

Run 26 Roll angles + pushes ?

11111111

-._--",,-- / ... __ .....

'I'''''''' 288

, I ' , 388

111111 , I ' , 488

Run 27 Roll angles + pushes .•. ? .....

T

"""I 581

""""'1""""'1""""'1""""'1 288 388 408 581

Run 28 Roll angles + pushes

? '"

.. , .......

~ . :---.. . :.,-.~

--. ----

I I 11 I I I I I I I I I I I I I 11 I 11

299 399

I I I I I I I I 11

499

I I I I I I I I 501


.......... -. , ~ ~

.•.. ,-.. ----'" ......... ,.-...... ~--•. -....... -~-'-.--......... -- ~--......... .-. ......-... " .... _.-.

I I I I I I I I I I I I I I I I I I I I I 111111111111111111

Run ?

290 309

30 Roll angles + pushes

....... J/

400 501

,.,...-....... -. ... ---....r'" '.

, L_.-. .' . -.. ..,-

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 200

Run 31 Roll angles + pushes .?

.l \ ... ,-


288

.--............

1111111111111111

399

angles -I- pushes

I I I I

498

I I I I I I I I 58'

\_. -"'-- j

1111111111" 111111111111111111111111111

299 3!lt9 499 59.

Run 33 Roll angles + pushes ?

..J,.- "-' ,/\ -+---'~O:-----"~~"--------=="7":--=,-+} ........ "'----r::---

. .-r-.r-. --_~ ....... _, .••.. ,--........ -...~ ................ _--......_~ ..... __ ~-_.-. _0- .• ,_............ ,; ", -'! .. ~-~.--...L-.-

.... l \.l

1"-I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I



2~Ht

111111111111111

380

¥F.35 RoU angles + pushes

r '-,. ..-., ~ " __ '.. , .. "r '_

11 I I I I I I I I I I I 400 501

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 11 I 11 I 200 3~0 400 501

Run 36 Roll angles + pushes:

'I

_.Jl

:,.,."" ... ,. .-.~ . I'~

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· 2011. 3. 31. · SUMMARY The Skill of Bicycle Riding A.J.R. Doyle The principal theories of human motor skill are compared. Disagreements between them centre around the exact